^  ^^^^^^ 


NEW  TREATISE 


USE  OF  THE  GLOBES; 


A  PHILOSOPHICAL  VIEW 


THE  EARTH  AND  HEAVENS: 

COMPREHENDING 

AN  ACCOUNT  OF  THE  FIGURE,    MAGNITUDE,  AND  MOTION    OF  THE  EARTH;  WITH 
THE  NATURAL  CHANGES  OF  ITS  SURFACE,  CAUSED  BY  FLOODS,  EARTH- 
QUAKES, &C.  TOGETHER  WITH  THE  PRINCIPLES  OF  METEOR- 
OLOGY, AND  ASTRONOMY  ;  WITH  THE  THEORY  OF 
THE  TIDES,  ETC. 

PRECEDED  BY 

AN  EXTENSIVE  SELECTION    OF  ASTRONOMICAL,  AND  OTHER   DEFINITIONS  J  AND 
ILLUSTRATED  BY  A  GREAT  VARIETY  OF  PROBLEMS,  QUESTIONS  FOR 
THE  EXAMINATION  OF  THE  STUDENT,  ETC.  ETC. 

DESIGNED  FOR  THE  INSTRUCTION  OF  YOUTH. 


BY  THOMAS  KEITH. 


REVISED  AND  CORRECTED, 

BY  ROBERT  ADRIAN,  LL.D.;  F.A.P.S.;  F.A.A.S.,  &c. 

AND  PROFESSOR  OF  MATHEMATICS  IN  RUTGER's  COLLEGE, 
NEW  BRUNSWICK,  NEW  JERSEY. 


NEW  YORK : 

SAMUEL  WOOD  &  SONS,  261  PEARL-STREET. 

1832. 


SOUTHERN  DISTRICT  OF  NEW- YORK,  ss. 

BE  IT  REMEMBERED,  That  on  the  Seventeenth  rlay  of  July,,  A.D.  1826,  in  the  fifty-first 
year  of  the  Independence  of  the  United  ^"tates  of  America,  J^amuel  Wood  <fc  Sons,  of  the  said 
District,  hath  deposited  in  this  oflice,  the  title  of  a  book,  the  right  whereof  they  claim  as  proprie- 
tors, in  the  words  following,  to  wit : 

A  new  Treatise  on  the  Use  of  the  Globes,  or  a  Philosophical  View  of  the  Earth  and  Heavens  : 
comprehending  an  account  of  the  figure,  magnitude,  and  motion  of  the  earth  ;  with  the  natural 
changes  of  its  surface,  caused  by  floods,  earthquakes,  &c.  togetlier  with  the  principles  of  meteor- 
oloay,  and  astronomy  ;  with  the  theory  of  the  tides,  &c.  Preceded  by  an  extensive  selection  of 
astronomical  and  other  definitions;  and  illustrated  by  a  great  variety  of  problems,  questions 
for  the  examination  of  the  student,  &c.  &c.  designed  for  the  instruction  of  youth.  By  Thomas 
Keith.  The  fourth  American  from  the  last  London  edition.  Revised  and  corrected  by  Robert 
Adrain,  LL.D.;  F  A.P.S.;  F.A.A.S.,  &c.  and  professor  of  mathematics  in  Ilutger's  College,  New 
Brunswick,  New  Jersey. 

In  conformity  to  the  Act  of  Congress  of  the  United  States,  entitled,  "An  Act  for  the  encourage- 
ment of  Learning,  by  securing  the  copies  of  Maps,  Charts,  and  Books,  to  the  authors  and  pro- 
prietors of  such  copies,  during  the  time  therein  mentioned,"  And  also  to  an  Act,  entitled,  "  An 
Act;  supplementary  to  an  Act,  entitled  '  An  act  for  the  encouragement  of  Learning,  by  securing 
the  copies  of  Maps,  Charts,  and  Books,  to  the  authors  and  proprietors  of  such  copies,  during  the 
times  therein  mentioned,'  and  extending  the  benefits  thereof  to  the  arts  of  designing,  engraving, 
and  etching  historical  and  other  prints." 

JAMES  DILL, 
Clerk  of  the  Southern  District  of  New- York. 


R.  &  G.  S.  WOOD,  PRINTERS. 


WILSON'S 

AMERICAN  GLOBES. 

[3,  9  AND   13  INCHES  IN  DIAMETER.] 


SAMUEL  WOOD  &  SONS, 

Agents  for  the  sale  of  Wilson's  American  Globes,  have  con- 
stantly on  hand  a  supply  of  different  sizes,  of  the  latest  manufacture. 
Great  pains  have  been  taken  in  the  execution  of  the  Plates  for  these 
Globes,  to  render  them  elegant  as  well  as  useful.  The  tracks  and 
discoveries  of  Columbus,  Cooke,  Vancouver,  Gore,  Butler,  Phipps, 
Parry,  &c.  are  carefully  delineated.  The  geographical  divisions  are 
taken  from  the  latest  charts  ;  and  in  respect  to  our  own  country,  they 
are  much  more  correct  tnan  the  Enghsh  globes. 

The  Celestial  contains  the  names  of  several  Constellations  that  are 
not  to  be  found  on  any  other  Globes, 

The  prices  of  these  Globes  are  much  lower  than  the  English  can 
be  imported  for,  and  the  style  of  finishing  quite  equal  if  not  superior; 
consequently  our  Schools  and  Academies  would  find  it  for  their 
interest  to  use  them. 


PREFACE. 


Amongst  the  various  branches  of  science  studied  in  our 
academies,  and  places  of  pubHc  education,  there  are  few  of 
greater  importance  than  that  of  the  Use  of  the  Globes.  The 
earth  is  our  destined  habitation,  and  the  heavenly  bodies  measure 
our  days  and  years  by  their  various  revolutions.  Without  some 
acquaintance  with  the  different  tracts  of  land,  the  oceans,  seas,  <fec. 
on  the  surface  of  the  terrestrial  globe,  no  intercourse  could  be 
carried  on  with  the  inhabitants  of  distant  regions,  and  conse- 
quently their  manners,  customs,  &c.  would  be  totally  unknown 
to  us.  Though  the  different  tracts  of  land,  &c.  cannot  be  so 
minutely  described  on  the  surface  of  a  terrestrial  globe  as  on 
different  maps ;  yet  the  globe  shows  the  figure  of  the  earth  and 
the  relative  situations  of  the  principal  places  on  its  surface, 
more  correctly  than  a  map.  Had  the  ancients  paid  no  attention 
to  the  motions  of  the  heavenly  bodies,  historical  facts  would 
have  been  given  without  dates,  and  we  should  have  had  neither 
dials,  clocks,  nor  watches.  To  the  celestial  observations  of 
Eudoxus,  Hipparchus,  &c.  we  are  indebted  for  the  knowledge 
of  the  precession  of  the  equinoxes.  Without  some  acquaintance 
with  the  celestial  bodies  our  ideas  of  the  power  and  wisdom  of 
the  Creator  would  be  greatly  circumscribed  and  confined.  The 
learned  and  pious  Dr.  Watts  observes,  "What  wonders  of 
Wisdom  are  seen  in  the  exact  regularity  of  the  revolutions  of  the 
heavenly  bodies  !  Nor  was  there  ever  any  thing  that  has  con- 
tributed to  enlarge  my  apprehensions  of  the  immense  power  of 
God,  the  magnificence  of  his  creation,  and  his  own  transcendent 


vi 


PREFACE. 


grandeur,  so  much  as  the  httle  portion  of  astronomy  which  I 
have  been  able  to  attain.  And  I  would  not  only  recommend  it 
to  young  students,  for  the  same  purposes,  but  I  would  persuade 
all  mankind,  if  it  were  possible,  to  gain  some  degree  of  acquaint- 
ance with  the  vastness,  the  distances,  and  the  motions  of  the  plan- 
etary worlds,  on  the  same  account." 

Dr.  Young,  in  his  Night  Thoughts,  says, 

"An  undevout  Astronomer  is  mad." 

There  is  scarcely  a  writer  on  the  different  branches  of  educa- 
tion who  has  not  expressly  recommended  the  study  of  the  globes. 
Milton  observes  that  "  ere  half  the  school  authors  be  read,  it  will 
be  seasonable  for  youth  to  learn  the  use  of  the  globes."  Yet 
notwithstanding  the  importance  of  the  subject,  it  is  entirely  neg- 
lected in  our  public  schools ;  and  in  many  of  our  private  acade- 
mies it  has  been  frequently  imperfectly  taught;  probably  for 
want  of  a  treatise  sufficiently  comprehensive  in  its  object,  and 
illustrated  by  a  suitable  number  of  examples. 

There  are  several  treatises  on  the  globes  extant,  but  they  have 
been  chiefly  written  by  mathematical  instrument  makers,*  or  by 


*  The  addition  of  a  few  wires,  a  semicircle  of  brass,  a  particular  kind  of  hour 
circle,  &c.  which  is  of  no  other  use  on  the  globe  than  to  enhance  the  price  thereof, 
has  generally  been  a  sufficient  inducement  for  the  instrument  maker  to  pubhsh  a 
treatise  explanatory  of  the  use  of  such  addition.  The  more  simply  the  globes  are 
fitted  up,  and  the  less  they  are  encumbered  with  useless  wires,  &c.  the  more  easily 
they  will  be  understood  by  the  generaUty  of  learners.  The  most  important  part  of 
a  globe  is  its  external  surface :  if  the  places  on  the  terrestrial  globe,  and  the  stars  on 
the  celestial,  be  accurately  laid  down,  and  distinctly  and  clearly  engraven,  it  is  of 
little  consequence  of  what  materials  the  frame  is  made. 

The  principal  globe  makers  in  London  are  Gary,  Bardin,  Newton,  and 
Addison. 

Gary's  globes  are  21  inches,  IS  inches,  15  inches,  12  inches,  and  9  inches  in 
diameter,  and  the  celestial  globe  may  be  purchased  either  with  or  without  the 
hieroglyphical  figures  depicted  on  the  surface. 

Bardin's  globes,  or,  as  they  are  usually  called,  the  New  British  Globes,  are 
18  inches,  and  12  inches  in  diameter.  The  New  British  Globes,  manufactured 
ntidet  th^  direetion  of  Messrs.  W.  ^  B.  JoneSy  Holborn,  are  particularly  recom- 


PREFACE. 


vii 


teachers  unacquainted  with  mathematics.  The  works  of  the 
former  must  be  defective  for  want  of  practice  in  the  art  of  teach- 
ing ;  and  many  of  the  productions  of  the  latter  are  too  peurile 
and  trifling  to  be  introduced  into  a  respectable  academy.  Youth 
learn  nothing  effectually,  but  by  frequent  repetition ;  a  multi- 
plicity of  examples  therefore  becomes  absolutely  necessary  ;  but 
these  examples  should  be  so  varied,  and  the  mode  of  proposing 
the  questions  so  diversified,  as  to  give  the  scholar  room  for  the 
exertion  of  his  faculties,  or  otherwise  no  impression  will  remain 
on  his  mind.  Treatises  on  the  globes  are  generally  either  with- 
out any  practical  exercises  ;  or  the  exercises  are  so  similar,  that 
when  the  pupil  has  finished  one  of  them,  the  rest  may  be  per- 
formed without  the  trouble  of  thinking.  Examples  of  this  kind 
may  serve  to  pass  away  the  time,  but  they  will  never  instruct  the 
scholar. 

Had  any  mathematical  writer  of  note  furnished  the  student 
with  a  treatise  on  the  globes,  the  following  work  would  probably 
have  never  appeared ;  but  it  rarely  happens  that  the  man  of 
science,  whose  whole  time  is  employed  in  abstruse  researches,  will 
stoop  to  the  humble  task  of  accommodating  himself  to  the  capa- 
city of  a  learner.    To  a  man  in  the  habit  of  contemplating  the 


mended  by  Mr.  Vince,  in  vol.  i.  page  569,  of  his  complete  System  of  Astronomy, 
and  were  introduced  into  the  Royal  Observatory  at  Greenwich,  by  the  late 
Dr.  Maskelyne. 

Newton's  globes  are  15  inches,  and  12  inches  in  diameter.  The  horizon  on 
these  globes  is  the  same  as  on  Bardin's;  only,  instead  of  the  signs  of  the  zodiac, 
the  ecliptic  and  zodiacal  constellations  are  introduced.  The  analemma  on  the 
surface  is  not  essentially  different  from  that  on  Gary's  globes. 

Addison's  globes  are  18,  12,  and  10  inches  in  diameter.  The  analemma  on  the 
surface  of  these  globes  is  the  same  as  the  analemma  on  Gary's  globes.  Mr.  Addi- 
son is  now  constructing  a  superb  pair  of  globes,  36  inches  in  diameter 

Wilson's  American  Globes  are  13  inches,  9  inches,  and  3  inches  in  diameter. 
They  are  used  in  academies  generally  in  preference  to  any  others,  as  they 
are  quite  equal  to  the  best  English  in  the  execution  of  the  plates ;  more  correct 
in  the  geographical  divisions  of  the  western  continent ;  and  can  be  purchased  at 
less  prices. 


viii 


PREFACE. 


writings  of  a  Newton,  or  travelling  in  the  dry  and  difficult  paths 
of  abstract  knowledge,  a  treatise  on  the  globes  is  a  mere  play- 
thing, a  trifle  not  worth  notice ;  as  at  one  glance  he  sees  and 
comprehends  every  problem  that  can  be  performed  by  them. 
Such  a  man  would  acquire  no  credit  by  writing  a  Treatise  on 
the  Globes ;  for,  notwithstanding  the  utility  of  the  subject,  its 
simplicity  would  leave  no  room  for  him  to  display  his  abilities : 
the  task,  therefore,  necessarily  devolves  on  writers  of  a  more 
humble  rank. 

The  ensuing  Treatise  has  been  formed  entirely  from  the  prac- 
tice of  Instruction,  and  is  arranged  in  the  following  order : 

Part  I.  The  definitions  are  very  extensive,  and,  it  is  hoped, 
sufficiently  plain  and  clear.  Where  the  name  cf  any  ancient 
author  occurs,  the  time  in  which  he  flourished,  and  his  country, 
are  generally  mentioned  in  a  note ;  this  practice  is  followed 
throughout  the  book.  The  table  of  climates  has  been  newly 
calculated,  and  the  principle  of  calculation  is  given  at  full  length. 
Thej^r^^  chapter  likewise  contains  a  table  of  the  constellations, 
with  the  fabulous  history  of  several  of  them ;  the  Greek  alpha- 
bet, &c.  If  the  definitions,  geographical  theorems,  &:c.  in  this 
chapter  be  well  explained  by  the  tutor,  it  is  presumed  that  the 
scholar  will  derive  considerable  advantage.  The  second  chapter 
contains  the  general  properties  of  matter,  and  the  laws  of  motion, 
as  preparatory  to  the  reading  of  the  third  and  fourth  chapters ; 
which  would  otherwise  be  less  intelligible.  To  the  third  and 
fourth  chapters  are  added  some  useful  notes,  which  ought  to  be 
attended  to  by  those  students  who  are  acquainted  with  arith- 
metic. Thejifth  chapter  treats  of  springs,  rivers,  and  the  saltness 
of  the  sea ;  the  sixth  of  the  tides  ;  and  the  seventh  of  earth- 
quakes, &c.  with  their  effects  and  causes.  The  subject  of  the 
eighth  chapter  is  the  atmosphere,  and  of  the  ninth,  meteorology. 
From  each  of  these  chapters,  it  is  hoped,  the  student  will  derive 
some  useful  information. 

It  has  not  been  usual  to  introduce  several  of  the  aforesaid 
subjects  into  a  Treatise  on  the  Globes.    An  intelligent  reader 


FUEFACE. 


ix 


will,  however,  readily  admit  them  to  be  less  extraneous,  equally 
entertaining,  and  more  instructive  than  scraps  of  poetry,  historical 
anecdotes,  &:c.  with  which  some  of  our  Treatises  on  the  Globes 
abound.  Poetical  scraps  seldom  elucidate  either  mathematical 
or  philosophical  subjects,  and  generally  divert  the  attention  of 
the  student  from  the  main  object  of  his  pursuit. 

Part  II.  This  part  comprehends  the  elementary  principles 
of  Astronomy,  including  an  account  of  the  solar  system.  These 
ought  to  be  clearly  understood  by  the  young  student  before  he 
attempts  to  solve  many  of  the  problems  in  the  succeeding  parts 
of  the  book.  The  object  in  learning  the  Use  of  the  Globes 
should  be  to  illustrate  some  of  the  most  important  branches  of 
geography  and  astronomy;  and  this  object  can  not  be  attained  by 
merely  tw^irling  the  globe  around  and  working  a  few  problems, 
without  understanding  the  principles  on  which  their  solutions 
are  founded.  Lessons  thoroughly  explained  and  clearly  under- 
stood make  a  lasting  impression  on  the  student's  memory,  and 
will  enable  him  not  only  to  solve  such  problems  as  he  may  meet 
with  in  books  on  the  Globes,  but  to  frame  several  new  problems 
himself,  and  to  solve  others  of  which  he  never  heard  before. 
^  In  the  notes  attached  to  this  part  of  the  following  work,  the 
distances,  magnitudes,  &c,  of  the  planets  are  all  accurately  cal- 
culated. This  laborious  task  the  author  would  gladly  have  avoid- 
ed, but  he  found  the  accounts  of  the  distances,  magnitudes,  &:c. 
of  the  planets  so  variable  and  contradictory,  even  in  astronomical 
works  of  repute,  and  frequently  in  the  same  author,  that  he  con- 
ceived such  notes  as  he  has  introduced  would  be  very  useful  to  a 
learner. 

Part  III.  Contains  an  extensive  collection  of  Problems; 
illustrated  by  a  great  number  of  useful  examples,  many  of  which 
are  elucidated  with  notes  of  considerable  importance. 

Part  IV.  Comprehends  a  miscellaneous  selection  of  Prob- 
lems, and  Questions  for  the  examination  of  the  student.  These 
questions  will  be  found  very  useful,  and  may  be  extended  with 
advantage  by  the  tutor. 

2 


X 


PREFACE. 


To  Conclude.  The  author  apprehends  that  he  has  omitted 
nothing  of  importance  that  particularly  relates  to  the  subject,  and 
he  hopes,  at  the  same  time,  that  this  work  will  be  found  to  con- 
tain little  or  no  extraneous  matter.  He  has  endeavoured  to  sup- 
ply the  young  student  with  a  Treatise  on  the  Globes,  which  may 
not  be  unworthy  of  attention,  as  a  work  of  science,  yet  suffi- 
ciently plain  and  intelligible. 


A  NEW  plate  was  delineated  for  the  second  edition  of  this  work 
showing  the  path  of  the  planet  Jupiter  in  the  Zodiac,  for  the  year 
1811,  which  will  likewise  answer  nearly  for  the  year  1823, 
together  with  the  constellations  and  principal  stars  through  which 
he  passes,  agreeably  to  their  appearance  in  the  heavens.  De- 
lineations of  this  kind  will  not  only  prove  amusing,  but  instruc- 
tive to  the  scholar,  as  they  give  a  more  correct  idea  of  the  rel- 
ative situations  of  the  stars  than  a  globe. 

By  laying  down  on  paper  all  the  principal  constellations  from 
the  celestial  globe,  as  directed  in  Problem  ClI. ;  rejecting  such 
stars  as  are  smaller  than  those  of  the  fourth  magnitude,  and  those 
constellations  w^hich  do  not  come  above  the  horizon,  the  young 
student  will  soon  render  the  appearance  of  the  heavens  familiar 
to  him. 

To  the  present  edition  several  wood  cuts  and  a  new  copper- 
plate have  been  added ;  the  whole  has  been  carefully  revised 
and  enlarged  by  a  considerable  quantity  of  additional  matter, 
with  a  view  of  rendering  it  as  complete  and  comprehensive  as 
possible.  1826. 


THE  CONTENTS. 


PART  I. 
CHAPTER  I. 


LINES  ON  THE  ARTIFICIAL  GLOBES,  ASTRONOMICAL  DEFINI- 
TIONS, GEOGRAPHICAL  THEOREMS,  &c. 


Def. 

Def. 

Pag-e 

Aberration 

121 

57 

Bootes 

49 

Acronical 

90 

45 

Brazen  Meridian  . 

5 

26 

Almacantars  . 

40 

33 

Altitude 

45 

34 

Canes  Venatici 

49 

Amplitude 

48 

34 

Cardinal  Points  24,  25, 

26  * 

31 

Amphiscii 

74 

41 

Cassiopeia 

50 

Andromeda  . 

49 

Camel  eopardalus  . 

50 

Angle  of  Position 

87 

44 

Canis  Minor 

52 

Antarctic  Pole 

4 

26 

Canis  Major 

52 

Antinous 

49 

Celestial  Globes 

2 

25 

Antipodes 

79 

41 

Cepheus 

50 

Antoeci 

77 

41 

Centrifugal  Force 

123 

58 

Aphelion 

110 

56 

Centripetal  Force 

122 

58 

Apogee 

108 

56 

Cerberus 

50 

Apparent  noon 

53 

35 

Cetus 

52 

Apsides 

112 

57 

Centaurus 

52 

Aquila 

49 

Chimbora^o  Mountain  (note) 

72 

Ara 

52 

Circles,  Great 

6 

26 

Arctic  Pole  . 

4 

26 

Circles,  Small 

7 

26 

Argo  Navis  ■. 

52 

Climate 

69 

38 

Ascension,  Right  . 

80 

4] 

Climate,  Tables  of 

39 

Ascension,  Oblique 

81 

42 

Colures 

14 

28 

Ascensional  Difference 

83 

42 

Coma  Berenices  : 

50 

Ascii 

74 

41 

Compass,  Mariners 

33  ! 

32 

Aspect  of  the  planets 

100 

56 

Constellation 

91,46 

126 

Asterion  et  Chara  . 

49 

Constellations,  a  Table  of 
Constellations,  Historical 

46 

Auriga  . 

49 

.  129 

Azimuth 

49 

34 

Account  of 

48 

Azimuth,  or  Vertical  Cir- 

Cor Caroli 

50 

cles 

43 

33 

Corvus 

53 

Axis  of  the  Earth  . 

3 

25 

Corona  Borealis 

50 

Bayer's  Characters  of  the 

Cosmical 

90 

45 

stars 

94 

54 

Crepusculum 

84 

42 

xii 


CONTENTS. 


Def. 

Crux  ... 

Culminating  Point  52 
Cygnus 

Day,  Astronomical  58 

Day,  Artificial       .  59 

 Civil      .       .  60 

 True  Solar     .  56 

  Mean  Solar    .  57 

 Siderial         .  61 

Declination           .  15 
Degree,  length  of  (note) 
Delphinus 

Descensional  Difference  83 

Digit      .       .       .  104 

Direct    ...  101 

Disc      ...  105 

Diurnal  Arc           .  119 

Divisibility 

Draco  ... 

Eccentricity  .  113 

Eclipse  of  the  Sun  116 
Eclipse  of  the  Moon  117 
Ecliptic  .  .  11 
Ellipsis  (note) 

Elongation     .       .  118 

Equator         .       .  10 

Equation  of  Time  55 

Equinoctial  Points  30 

Equulus 

Eridanus 

Extension 

Eudoxus  (note) 

Figure 

Fixed  Stars  .  89 

Foci  of  an  Ellipsis  (note)  . 
Force  ... 
Force,  Centrifugal  123 
Force,  Centripetal  122 

Galaxy  .       .  92 

Goencentric         .  106 
Geographical  Theorems 
Globe,  Celestial     .  2 
Globe,  Terrestrial  1 
Gravity 

Great  Circles  .  6 
Greek  Alphabet  . 

Heliacal  .  .  90 
Heliocentric  .  107 

Hemisphere  .  32 

Hercules 
Hesoid  (note) 
Heteroscii      .       .  75 
Himalaya  Mountains  ( note) 
Hipparchus  (note) 


Taie- 

Def. 

Page. 

53 

Historical  Account  of  the 

OO 

ClQ 
ZO 

.  OU 

TTnriynn  20  21  22 

*     OQ  n(\ 

.   ZVf  ov 

23 

.  oU 

DO 

T-Tnnr  f^irplp 

19 

OQ 

•  ztf 

.  DO 

ilour  Circles 

50 

DO 

OO 

.  OO 

.  OO 

OU 

.  OK) 

Latitude  of  a  place 

35 

?iO 

.  Oyi 

Latitude  of  a  Planet  or 

■  76 

Star 

36 

1  OO 

.  ou 

Leo  Minor 

.  ol 

42 

Lepus 

.  OO 

56 

Line  of  the  Apsides 

112 

57 

Ob 

Lines  of  Longitudes 

8 

CiCf 

i\R 

.  Ou 

Longitude  of  a  place 

38 

.  OO 

.            O  / 

Longitude  of  a  Planet  or 

Star 

39 

OO 

.  ou 

Lynx 

.  01 

Lyra 

Oi 

.  O/ 

.        o  / 

Mariner's  Compass  33  & 

c34 

^O 

.  oz 

57 

Matter,  General  Proper- 

27 

ties  of,  &c. 

.  oz 

1  o 

Mean  Noon 

54 

OO 

K.'y  ICC 
0/,  Ibo 

Meridians 

8 

zb 

Meridian,  Brazen 

5 

26 

OO 

Meridian,  First 

9 

oc 
zo 

31 

Microscopium 

53 

50 

Milky  Way  . 

92 

.  OO 

OO 

Mons  Msenalus 

.            0 1 

RO 

Monoceros 

K^ 

OO 

.  o/ 

Motion,  Absolute,  &c. 

R^ 

.  bo 

Motion,  General  Laws  of. 

RA 

•  b'l 

CO 

Motion,  Compound,  &c. 

RK 
OO 

'AO,  loo 

.          1  o 

Nadir  . 

28 

.           O I 

b'l 

Nebulous  Stars 

93 

KA 

.  04 

OO 

New  South  Shetland  (note) 

87 

Ol 

.  OO 

Nocturnal  Arc 

120 

KH 

.  o/ 

Nodes  of  a  Planet 

99 

.  Ob 

53 

Noon  Apparent 

53 

DO 

56 

Noon,  True  or  Mean 

54 

35 

59 

o  c 
zo 

Oblique  Ascension 

81 

'i.Z 

Of; 

Zo 

Oblique  Descension 

82 

AO 

.  bo 

Occultation  . 

114 

Kl 

.  Ol 

Of; 

Orbit  of  a  Planet 

98 

KK 

.  OO 

OO 

Orion 

K% 

.  OO 

46 

Parrallax 

86 

44 

56 

Parallels  of  Celestial  Lat 

- 

32 

tude 

41 

33 

50 

Parallels  of  Declinition 

42 

33 

37 

Parallels  of  Latitude 

18 

29 

41 

Pegasus 

51 

72 

Pendulum,  vibrating  sec- 

28, 37 

onds,  (note) 

73 

CONTENTS. 


xiii 


Def. 

Perigee  .  .  109 
Perihelion  .  .  Ill 
Perioeci  ,       .  78 

Periscii  .       .  76 

Perseus 

Piscis  Australis 
Planets        ,       95,  96,  97 
Pliny  Cnote) 

Poetical  rising  and  setting 

of  the  Stars  .  90 
Points,  Cardinal  24,  25  26 
Polar  Axis  of  the 

Earth  (note; 
Polar  Circles         .  17 
Polar  Distance       .  47 
Polar  Star  (note)  . 
Poles  of  the  Earth  4 
Pole  of  any  Circle  29 
Positions  of  the  Sphere  65 
Precession  of  the  Equi- 
noxes     .       .  64 
Prime  Vertical       .  44 

auadrant  of  Altitude  37 

Refraction  .  .  85 
Retrograde  .  .  103 
Rhumbs 
Right  Ascension  .  80 
Robur  Caroli 
Sagitta 

Scutum  Sobieski 
Serpens 
Serpentarius 


Page. 
56 
57 
41 
41 
51 
53 
55 
37 

45 
31 

74 
29 
34 

26,  133 
26 
31 
38 

37 
34 

33 

42 
56 
45 
41 
53 
51 
51 
51 
52 


Sextans 

Six  o'clock  Hour  Line 
Small  Circles 
Solidity 

Solstitial  Points 
Sphere  Positions  of  65, 

66,  67,  68 
Spheriod  (note) 
Stationary 


Def 

51 
7 

31 


102 


Taurus  Poniatowski 
Triangulum 

Transit  .  .  115 
Tropics  .  .  16 
Twilight        .       .  84 

Variation  of  the  Compass  34 
Velocity 


Vertical  Circles 
Via  Lactea 
Vis  Inertiae 
Vulpecula  et  Anser 

Ursa  Major 

Year,  Siderial 
Year,  Solar 


43 
92 


Zenith  .       .  27 

Zenith  Distance  .  46 
Zodiac  .       .  12 

Zodiacal  Signs  .  13 
Historical  Account  thereof 
Zones  70,  71,  72,  73 


53 
35 
26 
62 
31 

38 
73 
56 

52 
52 
57 
29 
42 

32 
64 
33 
53 
63 
52 

52,  131 

37 
37 

31 

34 
27 


40,41 


CHAP.  II.     Of  the  General  Properties  of  Matter  and  the  Laws  of  Motion 

III.  Of  the  Figure  of  the  Earth  and  its  Magnitude 

IV.  Of  the  Diurnal  and  Annual  Motion  of  the  Earth 

V.  Of  the  Origin  of  Springs  and  Rivers,  and  of  the  Saltness  of 

the  Sea 

VL  Of  the  Flux  and  Reflux  of  the  Tides 

VII.  Of  the  Natural  Changes  of  the  Earth,  caused  by  Mountains 

Floods,  Volcanoes,  and  Earthquakes 

VIII.  Of  the  Atmosphere,  Air,  Winds,  and  Hurricanes 

IX.  Of  Vapours,  Fogs,  Mists,  Clouds,  Dew,  &c.  . 

1.  Vapours 

2.  Fogs  and  Mists 

3.  Clouds 

4.  Dew 

5.  Rain 

6.  Snow  and  Hail 
^                 7.  Thunder  and  Lightning 

8.  The  Falling  Stars 

9.  Of  the  Ignus  Fatuus  . 

10.  Of  the  Aurora  Borealis 

11.  Of  the  Rainbow 


62 
70 
77 

84 


97 
106 
113 

113 
113 
113 
114 
114 
115 
115 
116 
117 
118 
118 


xiv 


CONTENTS. 


PART  11. 


THE  ELEMENTARY  PRINCIPLES  OF  ASTRONOMY. 


CHAP.  1.    The  General  Appearance  of  the  Heavens      .  .  .123 


II.  Of  the  Situation  of  the  principal  Constellations,  and  the  man- 

ner of  distinguishing  them  from  each  other  .  .  126 

III.  Of  the  Motion  of  the  Fixed  Stars  by  the  Precession  of  the 

Equinoxes,  by  Abberration,  and  by  the  Nutation  of  the 
Earth's  Axis;  their  proper  Motions,  Distance,  variable 
Appearance,  &c.  .....  133 

IV.  The  Method  of  Measuring  the  Altitudes,  Zenith,  Distances,  &c. 

of  the  Heavenly  Bodies,  including  a  Description  of  the 
Astronomical  Gluadrant,  Circular  and  Transit  Instrument  137 

V.  Of  the  Solar  System  .....  139 

L  Of  the  Sun     .  .  .  .  .  .140 

2.  Of  Mercury    ......  141 

3.  Of  Venus       ......  143 

4.  Of  the  Earth  and  the  Moon  .  .  .146 

5.  Of  Mars        .  .  ....  153 

6.  Of  Vesta        ......  154 

7.  Of  Juno         ......  155 

8.  Of  Ceres        ......  155 

9.  Of  Pallas       ......  155 

10.  Of  Jupiter  and  his  Satellites  .  .  .  155 

IL  Of  Saturn,  his  SatelUtes  and  Ring    .  .  .160 

12.  Of  the  Georgium  Sidus  and  his  Satellites     .  .  163 

VL  On  the  Nature  of  Comets  ;  the  Elongations,  Stationary  and 
Retrograde  Appearances  of  the  Planets ;  and  on  the  Eclipses 
of  the  Sun  and  Moon         ...  .164 

1.  On  Comets     ......  164 

2.  Of  the  Elongations,  &c.  of  the  Interior  Planets        .  165 

3.  Of  the  Stationary  and  Retrograde  Appearances  of  the 

Exterior  Planets       .....  167 

4.  On  Solar  and  Lunar  Eclipses  .  .  .  167 
General  Observations  on  Eclipses  .  .  .  169 
Number  of  Echpses  in  a  Year    ....  170 

VII.  Of  the  Calendar  171 

1.  The  Cycle  of  the  Moon  .          .          .  .171 

2.  The  Epact      .  .          .          .          .  .^171 

3.  The  Cycle  of  the  Sun  .          .          .  .172 

4.  The  number  of  Direction       ....  173 

5.  To  find  the  Paschal  Full  Moon  by  the  Epact  .  174 

6.  Of  the  Year  by  the  Gregorian  Account       .  .  177 


CONTENTS. 


XV 


FART  III. 

PROBLEMS  PERFORMED  BY  THE  TERRESTRIAL  GLOBE. 


PROBLEM  L    To  find  the  Latitude  of  any  given  place,  178 

PROBLEM  IL    To  find  all  those  places  which  have  the  same  Latitude  as 

any  given  place  179 

PROBLEM  IIL    To  find  the  Longitude  of  any  place,  179 

PROBLEM  IV.    To  find  all  those  places  that  have  the  same  Longitude 

as  a  given  place,  180 

PROBLEM  V.    To  find  the  Latitude  and  Longitude  of  any  place,  181 

PROBLEM  VI.    To  find  any  place  on  the  Globe,  having  the  Latitude  and 

Longitude  of  that  place  given,  181 

PROBLEM  VIL    To  find  the  difference  of  Latitude  between  any  two 

places,  182 

PROBLEM  VIII.    To  find  the  difference  of  Longitude  between  any  two 

places,  183 

PROBLEM  IX.    To  find  the  distance  between  any  two  places,  184 

PROBLEM  X.    A  place  being  given  on  the  Globe,  to  find  all  places  which 

are  situated  at  the  same  distance  from  it  as  any  other  given  place,  187 

PROBLEM  XI.    Given  the  Latitude  of  a  place  and  its  distance  from  a 

given  place,  to  find  that  place  whereof  the  latitude  is  given,  188 

PROBLEM  XII.    Given  the  Longitude  of  a  place,  and  its  distance  from  a 

given  place,  to  find  that  place  whereof  the  Longitude  is  given,  189 

PROBLEM  XIII.    To  find  how  many  Miles  make  a  Degree  of  Longitude 

in  any  given  parallel  of  latitude,  190 

PRO]^EM  XIV.  To  find  the  bearing  of  one  place  from  another,  191 

PROBLEM  XV.    To  find  the  Angle  of  position  between  two  places,  192 


CONTENTS. 


Page. 

PROBLEM  XVI.    To  find  the  AntcEci,  Periceci,  and  Antipodes  to  the 

inhabitants  of  any  place,  194 

PROBLEM  XVIL  To  find  at  what  rate  per  hour  the  inhabitants  of  any 
given  place  are  carried  from  West  to  East,  by  the  Revolution  of  the 
Earth  on  its  Axis,  195 

PROBLEM  XVIIL    A  particular  place  and  the  hour  of  the  day  at  that 

place  being  given,  to  find  what  hour  it  is  at  any  other  place,  196 

PROBLEM  XIX.  A  particular  place  and  the  hour  of  the  day  being  given, 
to  find  all  places  on  the  Globe  where  it  is  then  noon,  or  any  other 
given  hour  197 

PROBLEM  XX.    To  find  the  Sun's  Longitude  (commonly  called  the 

Sun's  place  in  the  echptic)  and  his  declination,  199 

PROBLEM  XXI.    To  place  the  Globe  in  the  same  situation  with  respect 
to  the  Sun,  as  the  Earth  is  at  the  Equinoxes,  at  the  Summer  Solstice, 
and  at  the  Winter  Solstice,  and  thereby  to  show  the  comparative  * 
lengths  of  the  longest  and  shortest  days,  200 

PROBLEM  XXIL  To  place  the  Globe  in  the  same  situation  with  respect 
to  the  Polar  Star  in  the  Heavens,  as  the  Earth  is  to  the  inhabitants 
of  the  Equator,  &c.  viz.  to  illustrate  the  three  positions  of  the  Sphere, 
Right,  Parallel,  and  Oblique,  so  as  to  show  the  comparative  lengths 
of  the  longest  and  shortest  days,  205 

PROBLEM  XXm.  The  month  and  day  of  the  month  being  given,  to 
find  all  places  of  the  Earth  where  the  Sun  is  vertical  on  that  day; 
those  places  where  the  Sun  does  not  set,  and  those  places  where  he 
does  not  rise  on  the  given  day,  209 

PROBLEM  XXIV.  A  place  being  given  in  the  Torrid  Zone,  to  find 
those  two  days  of  the  year  on  which  the  Sun  will  be  Vertical  at  that 
place,  210 

PROBLEM  XXV.  The  month  and  day  of  the  month  being  given  (at  any 
place  not  in  the  Frigid  Zones),  to  find  what  other  day  of  the  year  is 
of  the  same  length,  211 

PROBLEM  XXVL    The  month,  day,  and  hour  of  the  day  being  given, 

to  find  where  the  Sun  is  Vertical  at  that  instant,  212 

PROBLEM  XXVII.  The  month,  day,  and  hour  of  the  day  at  any  place 
being  given,  to  find  all  those  places  of  the  Earth  where  the  Sun  is 
rising,  those  places  where  the  Sun  is  setting,  those  places  that  have 
noon,  that  particular  place  where  the  Sun  is  vertical,  those  places 
that  have  morning  twihght,  those  places  that  have  evening  twilight, 
and  those  places  that  have  midnight,  213 


CONTENTS.  *  XVU 

Page 

PROBLEM  XXVIII.  To  find  the  time  of  the  Sun's  rising  and  setting, 
and  the  length  of  the  day  and  night  at  any  place  not  in  the  Frigid 
Zones,  215 

PROBLEM  XXIX.  The  length  of  the  day  at  any  place,  not  in  the  Frigid 
Zones,  being  given,  to  find  the  Sun's  declination,  and  the  day  of  the 
month,  217 

PROBLEM  XXX.    To  find  the  length  of  the  longest  day  at  any  place  in 

the  North  Frigid  Zone,  219 

PROBLEM  XXXI.    To  find  the  length  of  the  longest  night  at  any  place 

in  the  North  Frigid  Zone,  220 

PROBLEM  XXXII.  To  find  the  number  of  days  which  the  Sun  rises  and 

^  sets  at  any  place  in  the  North  Frigid  Zone,  221 

PROBLEM  XXXIII.  To  find  in  what  degree  of  north  latitude  on  any 
day  between  the  21st  of  March  and  the  2 1st  of  June,  or  in  what 
degree  of  south  latitude,  on  any  day  between  the  23d  of  September 
and  the  21st  of  December,  the  Sun  begins  to  shine  constantly  with- 
out setting  ;  and  also  in  what  latitude  in  the  opposite  hemisphere  he 
begins  to  be  totally  absent,  223 

PROBLEM  XXXIV.  Any  number  of  days,  not  exceeding  182,  being 
given,  to  find  the  parallel  of  north  latitude  in  which  the  Sun  does  not 
set  for  that  time,  223 

PROBLEM  XXXV.  To  find  the  beginning,  end,  and  duration  of  twilight 

at  any  place  on  any  given  day,  224 

PROBLEM  XXXVI.    To  find  the  beginning,  end,  and  duration  of  con- 

stant  day  or  twilight  at  any  place,  226 

PROBLEM  XXXVII.    To  find  the  duration  of  twilight  at  the  North 

Pole,  227 

PROBLEM  XXXVIII.    To  find  in  what  climate  any  given  place  on  the 

Globe  is  situated,  227 

PROBLEM  XXXIX.  To  find  the  breadths  of  the  several  chmates  be- 
tween the  Equator  and  the  Polar  Circles,  228 

PROBLEM  XL.    To  find  that  part  of  the  equation  of  Time  which 

depends  on  the  obliquity  of  the  Ecliptic,  229 

PROBLEM  XLL    To  find  the  Sun's  meridian  altitude  at  any  time  of  the 

year  at  any  given  place,  231 

PROBLEM  XLIL    When  it  is  midnight  at  any  place  in  the  Temperate 
or  Torrid  Zones,  to  find  the  Sun's  altitude  at  any  place  (on  the  same 
'  meridian)  in  the  north  Frigid  Zone,  where  the  sun  does  not  descend 
below  the  horizon,  233 


3 


xviii 


CONTENTS. 


Page, 

PROBLEM  XLIII.   To  find  the  Sun's  amplitude  at  any  place,  234 

PROBLEM  XLIV.    To  find  the  Sun's  azuTiuth  and  his  altitude  at  any 

place,  the  day  and  hour  being  given,  235 

PROBLEM  XLV.  The  latitude  of  the  place,  day  of  the  month,  and  the 
sun's  altitude  being  given,  to  find  the  sun's  amizuth  and  the  hour  of 
the  day,  237 

PROBLEM  LXVL    Given  the  latitude  of  the  place,  and  the  day  of  the 

month,  to  find  at  what  hour  the  sun  is  due  east  or  west,  238 

PROBLEM  XLVIL    Given  the  sun's  meridian  altitude  and  the  day  of 

the  month,  to  find  the  latitude  of  the  place,  239 

PROBLEM  XLVIIL  The  length  of  the  longest  day  at  any  place,  not 
within  the  Polar  Circles,  being  given,  to  find  the  latitude  of  that 
place,  241 

PROBLEM  LXIX.  The  latitude  of  a  place,  and  the  day  of  the  month 
being  given,  to  find  how  much  the  sun's  declination  must  increase  or 
decrease  towards  the  elevated  pole,  to  make  the  day  an  hour  longer 
or  shorter  than  the  given  day,  242 

PROBLEM  L.  To  find  the  sun's  right  ascension,  oblique  ascension, 
oblique  descension,  ascensional  difference,  and  time  of  rising  and 
setting  at  any  place,  243 

PROBLEM  LL    Given  the  day  of  the  month,  and  the  sun's  amplitude, 

to  find  the  latitude  of  the  place  of  observation,  245 

PROBLEM  LIL    Given  two  observed  altitudes  of  the  sun,  the  time 

elapsed  between  them,  and  the  sun's  declination,  to  find  the  latitude,  246 

PROBLEM  LIIL    The  day  and  hour  being  given  when  a  solar  eclipse 

will  happen,  to  find  where  it  will  be  visible,  247 

PROBLEM  LIV.  The  day  and  hour  being  given  when  a  lunar  eclipse  will 

happen  to  find  where  it  will  be  visible,  248 

PROBLEM  LV.  To  find  the  time  of  the  year  when  the  Sun  or  Moon  will 

be  hable  to  be  echpsed,  252 

PROBLEM  LVL    To  explain  the  phenomenon  of  the  Harvest  Moon,  253 

PROBLEM  LVIL  The  day  and  hour  of  an  eclipse  of  any  one  of  the 
Satellites  of  Jupiter  being  given,  to  find  upon  the  Globe  all  those 
places  where  it  will  be  visible,  255 

PROBLEM  LVIIL    To  place  the  Terrestrial  Globe  in  the  sun-shine,  so 

that  it  may  represent  the  natural  position  of  the  Earth,  257 

PROBLEM  LIX.    The  latitude  of  a  place  being  given,  to  find  the  hour  of  268 
the  day  at  any  time  when  the  sun  ghines, 


CONTENTS.  XIX 

Page 

PROBLEM  LX.    To  find  the  sun's  altitude,  by  placing  the  Globe  in  the 

sunshine,  259 

PROBLEM  LXL    To  find  the  Sun's  declination,  his  place  in  the  ecliptic, 

and  his  azimuth,  by  placing  the  globe  in  the  sunshine,  2§P 

PROBLEM  LXIL    To  draw  a  meridian  line  upon  a  horizontal  plane,  and 

to  determine  the  four  cardinal  points  of  the  horizon,  260 

PROBLEM  LXIIL    To  form  a  horizontal  dial  for  any  latitude,  262 

PROBLEM  LXIV.    To  make  a  vertical  dial  facing  the  south,  in  north 

latitude,  264 


IL    PROBLEMS  PERFORMED  BY  THE  CELESTIAL  GLOBE. 

PROBLEM  LXV.    To  find  the  right  ascension  and  declination  of  the 

sun,  or  of  a  star,  268 

PROBLEM  LXVL    To  find  the  latitude  and  longitude  of  a  Star,  269 

PROBLEM  LXVIL  The  right  ascension  and  declination  of  a  star,  the 
moon,  a  planet,  or  of  a  comet,  being  given,  to  find  its  place  on  the 
Globe,  270 

PROBLEM  LXVIII.    The  latitude  and  longitude  of  the  moon,  a  star,  or 

a  planet  given,  to  find  its  place  on  the  Globe,  270 

PROBLEM  LXIX.    The  day  and  hour,  and  the  latitude  of  a  place  being 

given,  to  find  what  stars  are  rising,  setting,  culminating,  &c.  271 

PROBLEM  LXX.  The  latitude  of  a  place,  day  of  the  month,  and  hour 
being  given,  to  place  the  Globe  in  such  a  manner  as  to  represent  the 
Heavens  at  that  time,  in  order  to  find  out  the  relative  situations  and 
names  of  the  Constellations  and  remarkable  Stars,  273 

PROBLEM  LXXL    To  find  when  any  Star  or  Planet,  will  rise,  come  to 

the  meridian,  and  set  at  any  given  place,  273 

PROBLEM  LXXIL  To  find  the  ampfitude  of  any  Star,  its  oblique  ascen- 
sion and  descension,  and  its  diurnal  arc,  for  any  given  day,  274 

PROBLEM  LXXin.  The  latitude  of  a  place  given,  to  find  the  time  of  the 
year  at  which  any  known  star  rises  or  sets  acronically,  that  is,  when 
it  rises  or  sets  at  sun-setting,  275 

PROBLEM  LXXIV.  The  latitude  of  a  place  given,  to  find  the  time  of 
the  year  at  which  any  known  star  rises  or  sets  cosmically,  that  is, 
when  it  rises  or  sets  at  sun-rising,  276 


CONTENTS, 


Page. 

PROBLEM  LXXV.    To  find  Ihe  time  of  the  year  when  any  given  star 

rises  or  sets  heliacally,  277 

PROBLEM  LXXVL  The  latitude  of  a  place  and  day  of  the  month  being 
given,  to  find  all  those  stsrs  that  rise  and  set  acronically,  cosmically, 
and  hehacally,  279 

PROBLEM  LXXVn.    To  illustrate  the  precession  of  the  Equinoxes,  281 

PROBLEM  LXXVIIL   To  find  the  distances  of  the  stars  from  each  other 

in  degrees,  282 

PROBLEM  LXXIX.    To  find  what  stars  lie  in  or  near  the  Moon's  path, 

or  what  stars  the  Moon  can  eclipse,  or  make  a  near  approach  to,  283 

PROBLEM  LXXX.    Given  the  latitude  of  the  place  and  the  day  of  the 

month,  to  find  what  planets  will  be  above  the  horizon  after  sun-setting,  284 

PROBLEM  LXXXI.  Given  the  latitude  of  the  place,  day  of  the  month, 
and  hour  of  the  night  or  morning,  to  find  what  planets  will  be  visible 
at  that  hour,  284 

PROBLEM  LXXXII.  The  latitude  of  the  place  and  day  of  the  month 
given,  to  find  how  long  Venus  rises  before  the  Sun  when  she  is  a 
morning  star,  and  how  long  she  shines  after  the  Sun  sets  when  she  is 
an  evening  star,  285 

PROBLEM  LXXXIII.    The  latitude  of  a  place,  and  day  of  the  month 

being  given,  to  find  the  meridian  altitude  of  any  star  or  planet,  287 

PROBLEM  LXXXIV,    To  find  all  those  places  on  the  Earth  to  which 

the  Moon  will  be  nearly  vertical  on  any  given  day,  288 

PROBLEM  LXXXV.  Given  tlie  latitude  of  a  place,  day  of  the  month, 
and  altitude  of  a  star,  to  find  the  hour  of  the  night,  and  the  star's 
azimuth,  289 

PROBLEM  LXXXVL    Given  the  latitude  of  a  place,  day  of  the  month, 

and  hour  of  the  day,  to  find  the  altitude  of  any  star,  and  its  azimuth,  290 

PROBLEM  LXXXVIL  Given  the  latitude  of  a  place,  day  of  the  month, 
and  azimuth  of  a  star,  to  find  the  hour  of  the  night,  and  the  star's 
altitude,  291 

PROBLEM  LXXXVTIL  Two  stars  being  given,  the  one  on  the  meridian, 
and  the  other  on  the  east  or  west  part  of  the  horizon,  to  find  the 
latitude  of  the  place,  292 

PROBLEM  LXXXIX.  The  latitude  of  the  place,  the  day  of  the  month, 
and  two  stars  that  have  the  same  azimuth,  being  given,  to  find  the 
hour  of  the  night,  293 

PROBLEM  XC.  The  latitude  of  the  place,  the  day  of  the  month,  and  two 
stars  that  have  the  same  altitude,  being  given,  to  find  the  hour  of  the 
night,  '  294 


CONTENTS. 


xxi 


PROBLEM  XCI.    The  altitudes  of  two  stars  having  the  same  azimuth, 
and  that  azimuth  being  given,  to  find  the  latitude  of  the  place, 

PROBLEM  XCIL    The  day  of  the  month  being  given,  and  the  hour  when 
any  known  star  rises  or  sets,  to  find  the  latitude  of  the  place, 

PROBLEM  XCIIL  To  find  on  what  day  of  the  year  any  given  star  passes 
the  meridian  at  any  given  hour, 

PROBLEM  XCIV.    The  day  of  the  month  being  given,  to  find  at  what 
hour  any  given  star  comes  to  the  meridian, 

PROBLEM  XCV.    Given  the  azimuth  of  a  known  star,  the  latitude,  and 
the  hour,  to  find  the  star's  altitude  and  the  day  of  the  month. 


Page. 
294 

295 

296 
297 


PROBLEM  XCVL    The  altitudes  of  two  stars  being  given,  to  find  the 

latitude  of  the  place,  299 

PROBLEM  XCVn.    The  meridian  altitude  of  a  known  star  being  given, 

at  any  place  in  north  latitude,  to  find  the  latitude,  300 

PROBLEM  XCVIIL  The  latitude  of  a  place,  day  of  the  month,  and  hour 
of  the  day  being  given,  to  find  the  nonagesimal  degree  of  the  echptic, 
its  altitude  and  azimuth,  and  the  medium  cceli,  30O 

PROBLEM  XCIX.  The  latitude  of  a  place,  day  of  the  month,  and  the 
hour,  together  with  the  altitude  and  azimuth  of  a  star,  being  given, 
to  find  the  star,  302 

PROBLEM  C.  To  find  the  time  of  the  Moon's  southing,  or  coming  to  the 

meridian  of  any  place,  on  any  given  day  of  the  month,  30S 

PROBLEM  CL  The  day  of  the  month,  latitude  of  the  place,  and  the  time 
of  high  water  at  the  full  and  change  of  the  Moon,  being  given,  to 
find  the  time  of  high  water  on  the  given  day,  304 

PROBLEM  OIL    To  describe  the  apparent  path  of  any  planet,  or  of  a 

Comet,  amongst  the  fixed  stars,  &c.  308 


PROBLEMS  WHICH  MAY  BE  PERFORMED  BY  EITHER  GLOBE. 


XX. 

Page. 
199 

] 

Page. 

Page. 

PROB.  XXXVII. 

227 

PROB. 

XLIX. 

242 

XXV. 

211 

(( 

XXXVIII. 

227 

(C 

L. 

243 

XXVIII. 

215 

(( 

XXXIX. 

228 

<c 

LI. 

245 

XXIX. 

217 

<( 

LX. 

229 

<( 

LII. 

246 

XXX. 

219 

<( 

LXI. 

231 

(( 

LV. 

252 

XXXI. 

220 

(( 

XLIII. 

234 

«  . 

LVI. 

253 

XXXII. 

221 

(( 

XLIV. 

235 

(( 

LIX. 

258 

XXXIII. 

223 

« 

XLV. 

237 

(( 

LX. 

259 

XXXIV. 

223 

(( 

XL  VI. 

238 

(( 

LXI. 

260 

XXXV. 

224 

u 

XL  VII. 

239 

(( 

XXXVI. 

226 

(( 

XLVIII. 

241 

« 

xxii 


CONTENTS. 


PART  IV. 

Page 

A  promiscuous  collection  of  examples  exercising  the  problems  on  the 

Globes,  310  to  319 

A  collection  of  questions,  with  references  to  the  pages  where  the  answers 
will  be  found  ;  designed  as  an  assistant  to  the  tutor  in  the  examin- 
ation of  the  student,  320  to  334 


INDEX  TO  THE  TABLES. 

I.    A  table  of  climates,  39 

IL  Tables  of  the  Constellations,  alphabetically  arranged,  with  the 
number  of  stars  in  each  constellation,  and  the  names  of  the  prin- 
cipal stars  ;  together  with  the  right  ascension  and  declination  of 
the  middle  of  each  constellation,  for  the  ready  finding  of  them  on 
the  Globe,  46,  47,  48 

III.  A  table  of  the  velocity  and  pressure  of  the  winds,  112 

IV.  A  table  of  the  time  of  culminating  of  the  zodiacal  constellations  on 

the  first  day  of  every  month,  and  the  semi-diurnal  arc  atLondon,  127 

V.  A  table  of  the  satellites  of  Jupiter,  157 

VI.  A  table  of  the  configurations  of  the  satellites  of  Jupiter,  159 

VII.  A  table  of  the  satellites  of  Saturn,  162 

VIII.  A  table  of  the  Epacts  till  the  year  1900,  172 

IX.  A  table  showing  the  number  of  direction  for  finding  Easter  Sunday,  173 

X.  A  table  for  finding  Easter  till  the  year  1900,  174 

XI.  A  table  for  finding  the  moon's  age,  and  the  times  of  new  and  full 

moon,  till  the  year  1900,  176 

XII.  A  table  of  the  number  of  geographical  and  English  miles  which 

make  a  degree  in  any  given  parallel  of  latitude,  187 


XIII.    A  table  of  the  equation  of  time,  dependent  on  the  obliquity  of  the 
ecliptic,  for  every  degree  of  the  sun's  longitude, 


230 


CONTENTS.  XXIU 

Page, 

XIV.  A  table  of  all  the  visible  eclipses  which  will  happen  in  the  present 

century,  250 

XV.  A  table  of  the  hour  arcs  and  angles  for  a  horizontal  dial  for  the 

latitude  of  London,  264 

XVI.  A  table  of  the  hour  arcs  and  angles  for  a  vertical  dial  for  the  lati- 

tude of  London,  266 

XVII.  A  table  of  the  equation  of  time,  to  be  placed  on  a  sun-dial,  267 

XVIII.  A  table  of  the  time  of  high  water  at  new  and  full  moon,  at  the 
principal  places  in  the  British  Islands,  307 


SIX  COPPER-PLATES  TO  BE   PLACED  AT  THE   END  OF  THE  BOOK, 


NEW  TREATISE 

ON  THE 

USE  OF  THE  GLOBES,  &c. 


PART  I. 

DEFINITIONS  AND  INTRODUCTORY  SUBJEf3TS. 

CHAPTER  I. 

Explanation  of  the  Lines  on  tlie  Artificial  Globes,  including  Geo- 
graphical and  Astronomical  Definitions ;  with  a  few  Geograph" 
iced  Theorems, 

1.  THE  Terrestrial  Globe  is  an  artificial  representation  of 
the  earth.  On  this  globe  the  four  quarters  of  the  world,  the  dif- 
ferent empires,  kingdoms  and  countries;  the  chief  cities,  seas, 
rivers,  &c.  are  truly  represented,  according  to  their  relative  sit- 
uation on  the  real  globe  of  the  earth.  The  diurnal  motion  of  this 
globe  is  from  west  to  east. 

2.  The  Celestial  Globe  is  an  artificial  representation  of  the 
heavens,  on  which  the  stars  are  laid  down  in  their  natural  situa- 
tions. The  diurnal  motion  of  this  globe  is  from  east  to  west,  and 
represents  the  apparent  diurnal  motion  of  the  sun,  moon,  and 
stars.  In  using  this  globe,  the  student  is  supposed  to  be  situated  ^ 
in  the  centre  of  it,  and  viewing  the  stars  in  the  concave  surface. 

3.  The  Axis  of  the  Earth  \See  Plate  I.  ^Figures  I.  and  H.] 


*  Figure  I.  represents  the  frame  of  the  globe,  with  the  horizon,  brass  meridian, 
and  axis :  Figure  II.  the  Globe  itself,  with  the  hnes  on  its  surface. 

4 


26 


DEFINITIONS,  SlC, 


Part  I. 


is  an  imaginary  line  passing  through  the  centre  of  it,  upon  which  it 
is  supposed  to  turn,  and  about  which  all  the  heavenly  bodies  ap- 
pear to  have  a  diurnal  revolution.  This  line  is  represented  by 
the  wire  which  passes  from  north  to  south,  through  the  mi^ddle  of 
the  artificial  globe. 

4.  The  Poles  op  the  Earth  are  the  two  extremities  of  the 
axis,  where  it  is  supposed  to  cut  the  surface  of  the  earth,  one  of 
which  is  called  the  north,  or  arctic  pole ;  the  other,  the  south,  or 
antarctic  pole.  The  celestial  poles  are  two  imaginary  points*"  in 
the  heavens,  exactly  above  the  terrestrial  poles. 

5.  The  Brazen  Meridian  is  the  circle  in  which  the  artificial 
globe  turns,  and  is  divided  into  360  equal  parts,  called  degrees. f 
In  the  upper  semicircle  of  the  brass  meridian  these  degrees  are 
numbered  from  0  to  90,  from  the  equator  towards  the  poles,  and 
are  used  for  finding  the  latitudes  of  places.  On  the  lower  semi- 
circle of  the  brass  meridian  they  are  numbered  from  0  to  90,  from 
the  poles  towards  the  equator,  and  are  used  in  the  elevation  of 
the  poles. 

6.  Great  Circles  divide  the  globe  into  two  equal  parts,  as 
the  equator,  ecliptic,  and  the  colures. 

7.  Small  Circles  divide  the  globe  into  two  unequal  parts,  as 
the  tropics,  polar  circles,  parallels  of  latitude,  &:c. 

8.  Meridians,  or  Lines  of  Longitude,  are  semicircles,  extend- 
ing from  the  north  to  the  south  pole,  and  cutting  the  equator  at 
right  angles.  Every  place  upon  the  globe  is  supposed  to  have  a 
meridian  passing  through  it,  though  there  be  only  24  drawn  upon 
the  terrestrial  globe ;  the  deficiency  is  supplied  by  the  brass  me- 
ridian. When  the  sun  comes  to  the  meridian  of  any  place,  it  is 
noon  at  that  place. 

9.  The  First  Meridian  is  that  from  which  geographers  begin 
to  count  the  longitudes  of  places.  In  English  maps  and  globes 
the  first  meridian  is  a  semicle  supposed  to  pass  through  London, 
or  the  royal  observatory  at  Greenwich. 


*  The  polar  star  is  a  star  of  the  second  magnitude,  near  the  north  pole,  in  the 
end  of  the  tail  of  the  Little  Bear.  Its  mean  right  ascension,  for  the  beginning  of 
the  year  1820,  is  14°  13'  1"  ;  and  its  decHnation  88"  20'  55"  N.  Connoissance  des 
Terns,  for  1820,  p.  168. 

f  Every  circle  is  supposed  to  be  divided  into  360  equal  parts  called  degrees ;  each 
minute,  into  60  equal  parts  called  seconds,  &c. :  (a  degree  therefore  is  of  different 
lineal  extent,  according  to  the  magnitude  of  the  circumference  to  which  it  belongs. 
A  degree  of  a  great  circle  of  the  earth,  as  of  the  meridian  or  equator,  contains  60 
geographical  miles  or  69  1-10  English  miles.)  A  degree  of  a  great  circle  in  the 
heavens  is  a  space  nearly  equal  to  twice  the  apparent  diameter  of  the  sun  or  moon. 

Degrees  are  marked  with  a  small  cipher,  minutes  with  one  dash,  seconds  with 
twOf  thirds  with  three,  &c.  Thus  25°  14'  22"  35'",  are  read  25  degrees,  14  minutes, 
22  seconds,  35  thirds. 


Chap.  L 


DEFINITIONS,  &LC. 


27 


10.  The  Equator  is  a  great  circle  of  the  earth,  equi-distant  from 
the  poles,  and  divides  the  globe  into  two  hemispheres,  northern 
and  southern.  The  latitudes  of  places  are  counted  from  the 
equator,  northward  and  southward  ;  and  the  longitudes  of  places 
are  reckoned  upon  it,  eastward  and  w^estward. 

The  equator,  when  referred  to  the  heavens,  is  called  the  equi- 
noctial, because  when  the  sun  appears  in  it,  the  days  and  nights 
are  equal  all  over  the  world,  viz.  12  hours  each.  The  declinations 
of  the  sun,  stars,  and  planets,  are  counted  from  the  equinoctial 
northward  and  southw^ard,  and  their  right  ascensions  are  reckoned 
upon  it  eastward  round  the  celestial  giobe  from  0  to  360  degrees. 

11.  The  Ecliptic  is  a  great  circle  in  which  the  sun  makes  his 
apparent  annual  progress  among  the  fixed  stars* ;  or,  it  is  the 
great  circle  in  the  plane  of  which  is  situated  the  real  path  of  the 
earth  round  the  sun,  and  cuts  the  equinoctial  in  an  angle  of 
23°  28';  the  points  of  intersection  are  called  the  equinoctial  points. 
The  ecliptic  is  situated  in  the  middle  of  the  zodiac.  ^ 

To  show  that  the  great  circle  in  the  plane  of  which  is  situated  the  red  path  of 
the  earth  round  the  sun  is  the  same  as  the  apparent  path  of  the  sun  among  the 


fixed  stars,  let  S  represent  the  sun  ; 
when  the  earth  is  in  ^  Libra,  the 
sun  will  appear  in  T  «^nes ;  when 
the  earth  is  in  "ni.  Scorpio,  the  sun 
will  appear  in  ^  Taurus;  when 
the  earth  is  in  f  Sagittarius,  the 
sun  will  appear  in  JJ  Gemini;  and 
so  on  round  the  ecliptic.  The  eye 
cannot  judge  of  distances  beyond  a 
certain  limit ;  hence  the  heavenly 


bodies,  viz.  the  sun,  stars,  and  the  moon,  all  appear  c^wa/Zy  remote  from  a  spectator 
on  the  earth. 

12.  The  Zodiac,  on  the  celestial  globe,  is  a  space  which  extends 
about  eight  degrees  on  each  side  of  the  ecliptic,  like  a  belt  or  gir- 
dle, within  which  the  motions  of  all  the  planetsf  are  performed. 


*  The  sun's  apparent  diurnal  path  is  either  in  the  equinoctial  or  in  Hnes  nearly 
^parallel  to  it;  and  his  apparent  annual  path  may  be  traced  in  the  heavens,  by 
observing  what  particular  constellation  in  the  zodiac  is  on  the  meridian  at  mid- 
night; the  opposite  constellation  wHl  show,  very  nearly,  the  sun's  place  at  noon  on 
the  same  day. 

t  Except  the  new  discovered  planets,  or  Asteroids,  Ceres  and  Pallas. 


28 


DEFINITIONS,  &C. 


Part  I. 


13.  Signs  op  the  Zodiac.  The  ecliptic  and  zodiac  are  divid- 
ed into  12  equal  parts,  called  signs,  each  containing  3#  ^egr^es. 
The  sun  makes  his  apparent  annual  progress  through  the  ecliptic, 
at  the  rate  of  nearly  a  degree  in  a  day.  The  names  of  the  signs, 
and  the  days  on  which  the  sun  enters  them,  are  as  follows : 


Spring  Signs. 
T  Aries,  the  Ram,  21st  of 

March. 
«  Taurus,  the  Bull,  19th  of 

April. 

n  Gemini,  the  Twins,  20th 
of  May. 


Summer  Signs. 
Cancer,  the  Crab,  2 1st  of 
June. 

SI  Leo,  the   Lion,  22d  of 
July. 

n  Virgo,  the  Virgin,  22d  of 
August. 


These  are  called  northern  signs,  being  north  of  the  equinoctial. 


Autumnal  Signs. 
—  Libra,  the  Balance,  23d 

of  September, 
fll  Scorpio,  the  Scorpion,  23d 

of  October.  ' 
t  Sagittarius,   the  Archer, 

22d  of  November. 


Winter  Signs. 
V3  Capricornus,  the  Goat,  21st 
of  December. 
Aquarius,  the  Water-bearer, 
20th  of  January. 
^  Pisces,  the  Fishes,  19th  of 
February. 


These  are  called  southern  signs. 

The  winter  and  spring  signs  are  called  ascending  signs,  and  the 
summer  and  autumnal  signs  are  called  descending  signs. 

14.  The  Colures  are  two  great  circles  passing  through  the 
poles  of  the  world;  one  of  them  passes  through  the  equinoctial 
points,  Aries*  and  Libra ;  the  other,  through  the  solstitial  points. 
Cancer  and  Capricorn  ;  hence  they  are  called  the  equinoctial  and 
solstitial  colures.  They  divide  the  ecliptic  into  four  equal  parts, 
and  mark  the  four  seasons  of  the  year. 

15.  Declination  of  the  sun,  of  a  star,  or  planet,  is  its  distance 
from  the  equinoctial,  northward  or  southward.  When  the  sun  is 
in  the  equinoctial  he  has  no  declination,  and  enlightens  half  the 
globe  from  pole  to  pole.    As  he  increases  in  north  declination  he 


*  In  the  time  of  Hipparchus  the  equinoctial  cokire  is  supposed  to  have  passed 
through  the  middle  of  the  constellation  Aries.  Hipparchus  was  a  native  of  Nicasa, 
a  town  of  Bythinia,  in  Asia  Minor,  adout  75  miles  S.  E.  of  Constantinople,  now 
called  Isnicj  he  made  his  observations  between  160  and  135  years  before  Christ. 


Chap,  1. 


DEFINITIONS,  &C. 


29 


gradually  shines  farther  over  the  north  pole,  and  leaves  the  south 
pole  in  darkness :  in  a  similar  mannner,  w^hen  he  has  south  decli- 
nation, he  shines  over  the  south  pole,  and  leaves  the  north  pole  in 
darkness.  The  greatest  declination  the  sun  can  have  is  23 '  28' ; 
the  greatest  declination  a  star  can  have  is  90  ;  and  that  of  a 
planet  30>28'*  north  or  south. 

16.  The  Tropics  are  two  small  circles,  parallel  to  the  equator 
(or  equinoctial),  at  the  distance  of  23'  28'  from  it;  the  northern 
is  called  the  Tropic  of  Cancer,  the  southern  the  Tropic  of  Capri- 
corn. The  tropics  are  the  limits  of  the  torrid  zone,  northward 
and  southward. 

17.  The  Polar.  Circles  are  two  small  circles,  parallel  to  the 
equator  (or  equinoctial),  at  the  distance  of  66'  32'  from  it,  and 
23°  28'  from  the  poles.  The  northern  is  called  the  arctic^  the 
southern  the  antarctic  circle. 

18.  Parallels  of  Latitude  are  small  circles  drawn  through 
every  ten  degrees  of  latitude,  on  the  terrestrial  globe,  parrallel  to 
the  equator.,  Every  place  on  the  globe  is  supposed  to  have  a 
parrallel  of  latitude  drawn  through  it,  though  there  are  generally 
only  sixteen  parallels  of  latitude  drawn  on  the  terrestrial  globe. 

19.  The  Hour  Circle  on  the  artificial  globes  is  a  small  circle 
of  brass,  with  an  index  or  pointer  fixed  to  the  north  pole ;  it  is  di- 
vided into  24f  equal  parts,  corresponding  to  the  hours  of  the  day, 
and  these  are  again  subdivided  into  halves  and  quarters.  The 
hour  circle,  when  placed  under  the  brass  meridian,  is  moveable 
round  the  axis  of  the  globe,  ^nd  the  brass  meridian,  in  this  case, 
answers  the  purpose  of  an  index. 

20.  The  Horizon  is  a  great  circle  which  separates  the  visible 
half  of  the  heavens  from  the  invisible;  the  earth  being  considered 
as  a  point  in  the  centre  of  the  sphere  of  the  fixed  stars.  Horizon, 
when  applied  to  the  earth,  is  either  sensible  or  rational. 

21.  The  Sensible,  or  visible  horizon,  is  the  circle  which 


*  Except  the  planets,  or  Asteroids,  Ceres  and  Pallas,  which  are  nearly  at  the 
same  distance  from  the  sun ;  the  former,  in  April  1802,  was  out  of  the  zodiac,  its 
latitude  being  15°  20'  N. 

t  Some  globes  have  two  rows  of  figures  on  the  index,  others  but  one.  On 
Bardiri's  JSTew  British  Globes  there  is  an  hour  circle  at  each  pole,  numbered  with 
two  rows  of  figures.  On  Adams'  common  globes  there  is  but  one  index  ;  and  on 
his  improved  globes  the  hours  are  counted  by  a  brass  wire  with  two  indexes  stand- 
ing over  the  equator.  The  form  of  the  hour  circle  is,  however,  a  matter  of  little 
consequence,  (provided  it  be  placed  under  the  brass  meridian,)  as  the  equator  will 
answer  every  purpose  to  which  a  circle  of  this  kind  can  be  applied. 


so 


DEFINITIONS,  &C. 


Part  I. 


bounds  our  view,  where  the  sky  appears  to  touch  the  earth  or 
sea.* 

22.  The  Rational,  or  true  horizon,  is  an  imaginary  plane, 
passing  through  the  centre  of  the  earth  parrallel  to  the  sensible 
horizon.  It  determines  the  rising  and  setting  of  the  sun,  stars, 
and  planets. 

23.  The  Wooden  Horizon,  circumscribing  the  artificial  globe, 
represents  the  rational  horizon  on  the  real  globe.  This  horizon 
is  divided  into  several  concentric  circles,  which  on  Bardin^s^ 
New  British  Globes  are  arranged  in  the  followinoj  order: 

The  First  is  marked  amplitude,  and  is  numbered  from  the  east 
towards  the  north  and  south,  from  0  to  90  degrees,  and  from  the 
west  towards  the  north  and  south  in  the  same  manner. 

The  Second  is  marked  azimuth,  and  is  numbered  from  the  north 
point  of  the  horizon  towards  the  east  and  west,  from  0  to  90  de- 
grees ;  and  from  the  south  point  of  the  horizon  towards  the  east 
and  west  in  the  same  manner. 

The  Third  contains  the  thirty-two  points  of  the  compass,  di- 
vided into  half  and  quarter  points.  The  degrees  in  each  point 
are  to  be  found  in  the  amplitude  circle. 

The  Fourth  contains  the  twelve  signs  of  the  zodiac,  with  the 
figure  and  character  of  each  sign. 

The  Fifth  contains  the  degrees  of  the  signs,  each  sign  compre- 
hending 30  degrees. 

The  Sixth  contains  the  days  of  the  month  ansv/ering  to  each 
degree  of  the  sun's  place  in  the  ecliptic. 

The  Seventh  contains  the  equatio'n  of  time,  or  difference  of  time 
shown  by  a  well-regulated  clock  and  a  correct  sun-dial.  When 
the  clock  ought  to  be  faster  than  the  dial,  the  number  of  minutes, 
expressing  the  difference,  is  followed  by  the  sign  + ;  when  the 


*  The  sensible  horizon  extends  only  a  few  miles ;  for  example,  if  a  man  of  6 
feet  high  were  to  stand  on  an  extensive  level,  or  on  the  surface  of  the  sea ;  the  ut- 
most extent  of  his  view,  upon  the  earth  or  the  sea,  would  be  about  three  miles. 
Thus,  if  h  be  the  height  of  the  eye  above  the  surface  of  the  sea,  and  d  the  diameter 
of  the  earth  in  feet,  then 

V   

d-j-  h  h,  will  nearly  show  the  distance  which  a  person  will  be  able  to  see, 
straght  forward.    KeitWs  Trigonometry,  Fourth  Edition,  Example  XLV.  page  S2. 

t  Gary's  Globes  have  a  different  division  of  the  wooden  horizon.  The  first 
circle,  or  that  nearest  to  the  globe,  is  numbered  from  the  east  and  west  towards 
the  north  and  south,  from  0  to  90  The  second  contains  the  thirty-two  points  of 
the  compass :  The  third,  the  signs  of  the  zodiac  :  The  fourth,  the  degrees  of  the 
signs :  The  fifth,  the  days  of  the  months :  The  sixth,  the  names  of  the  months. 
The  wooden  horizon  of  Adams'  Globes  is  divided  in  the  same  manner. 


Chap.  I. 


DEFINITIONS,  &LC. 


clock  or  watch  ought  to  be  slower,  the  number  of  minutes  in  the 
difference  is  followed  by  the  sign  — .  This  circle  is  peculiar  to 
the  New  British  Globes. 

The  Eighth  contains  the  twelve  calender  months. 

24.  The  Cardinal  Points  of  the  horizon  are  east,  west,  north, 
and  south. 

25.  The  Cardinal  Points  in  the  heavens  are  the  zenith,  the 
nadir,  and  the  points  where  the  sun  rises  and  sets. 

26.  The  Cardinal  Points  of  the  ecliptic  are  the  equinoctial 
and  solstitial  points,  which  mark  out  the  four  seasons  of  the  year  ; 
and  the  Cardinal  signs  are  T  Aries,  25  Cancer,  ~  Libra,  and  V3 
Capricorn. 

27.  The  Zenith  is  a  point  in  the  heavens  exactly  over  our 
heads,  and  is  the  elevated  pole  of  our  horizon. 

28.  The  Nadir  is  a  point  in  the  heavens  exactly  under  our 
feet,  being  the  depressed  pole  of  our  horizon,  and  the  zenith,  or 
elevated  pole,  of  the  horizon  of  our  antipodes. 

29.  The  Pole  of  any  circle  is  a  point  on  the  surface  of  the 
globe,  90  degrees  distant  from  every  part  of  that  circle  of  which 
it  is  the  pole.  Thus  the  poles  of  the  earth  are  90  degrees  from 
every  part  of  the  equator;  the  poles  of  the  ecliptic  (on  the  celes- 
tial globe)  are  90  degrees  from  every  part  of  the  ecliptic,  and 
23=  28'  from  the  poles  of  the  equinoctial,  consequently  they  are 
situated  in  the  arctic  and  antarctic  circles.  Every  circle  on  the 
globe,  whether  real  or  imaginary,  has  two  poles  diametrically 
opposite  to  each  other. 

30.  The  Equinoctial  Points  are*  Aries  and  Libra,  where 
the  ecliptic  cuts  the  equinoctial.  The  point  Aries  is  called  the 
vernal  equinox,  and  the  point  Libra  the  autumnal  equinox.  When 
the  sun  is  in  either  of  these  points,  the  days  and  nights  on  every 
part  of  the  globe  are  equal  to  each  other. 

3L  The  Solstitial  Points  are  Cancer  and  Capricorn.  When 
the  sun  is  in,  or  near,  these  points,  the  variation  in  his  greatest  al- 
titude is  scarcely  perceptible  for  several  days;  because  the  ecliptic 
near  these  points  is  almost  parallel  to  the  equinoctial,  and  there- 
fore the  sun  has  nearly  the  same  declination  for  several  days.— 


*  The  terms  Aries,  Libra,  &c.  primarily  denoted  the  constellations  of  the  zodiac: 
in  the  course  of  time  they  were  also  used  to  signify  the  twelve  equal  divisions  of 
the  ecliptic  called  signs;  and  in  several  works  on  the  Globes  and  Astronontiy, 
are  employed  to  indicate  the  first  points  of  these  signs.  This  variety  of  sig- 
nification is  perplexing  to  beginners,  and  injurious  to  perspicuity:  it  is  better 
to  say  that  the  equinoctial  and  solstitial  points  are  the  first  points  of  the  signs, 
Aries,  Libra,  &c. 


32 


DEFINITIONS,  &C. 


Part  1. 


When  the  sun  enters  Cancer,  it  is  the  longest  day  to  all  the  in- 
habitants on  the  north  side  of  the  equator,  and  the  shortest  day  to 
those  on  the  south  side.  When  the  sun  enters  Capricorn  it  is 
the  shortest  day  to  those  who  live  in  north  latitude. 

32.  A  Hemisphere  is  half  the  surface  of  the  globe ;  every 
great  circle  divides  the  globe  into  two  hemispheres.  The  horizon 
divides  the  upper  from  the  lower  hemisphere  in  the  heavens ;  the 
equator  separates  the  northern  from  the  southern  on  the  earth ; 
and  the  brass  meridian,  standing  over  any  place  on  the  terrestrial 
globe,  divides  the  eastern  from  the  western  hemisphere. 

33.  The  Mariner's  Compass  is  a  representation  of  the  hori- 
zon, and  is  used  by  seamen  to  direct  and  ascertain  the  course  of 
their  ships.  It  consists  of  a  circular  brass  box,  which  contains  a 
paper  card,  divided  into  32  equal  parts,  and  fixed  on  a  magnetical 
needle  that  always  turns  towards  the  north.  Each  point  of  the 
compass  contains  11"  15'  or  11  1-4  degrees,  being  the  32d  part  of 
360  degrees. 

34.  The  Variation  of  the  Compass  is  the  deviation  of  its 
points  from  the  corresponding  points  in  the  heavens.  When  the 
north  point  of  the  compass  is  to  the  east  of  the  true  north  point 
of  the  horizon,  the  variation  is  east ;  if  it  be  to  the  west,  the  vari- 
ation is  west. 


The  learner  is  to  understand,  that  the  compass  does  not  always  point  directly 
north,  but  is  subject  to  a  small  (irregular)  annual  variation.  At  present,  in  Eng- 
land, the  needle  points  about  24^  degrees,  to  the  M^estward  of  the  north. 


At  London  in 

1576, 

the  variation  was. 

W 

15'  E. 

1747, 

17° 

40' W. 

1612, 

6 

10  E. 

1780, 

22 

10  W. 

1623, 

6 

0  E. 

1790, 

23 

39  W. 

1634, 

4 

5  E. 

1794, 

23 

54  W. 

1657, 

0 

0 

1796, 

24 

0  W. 

1666, 

1 

35  W. 

1800, 

24 

2  W. 

16S3, 

4 

30  W. 

1804, 

24 

8  W. 

1700, 

8 

0  W. 

1806, 

24 

8  W. 

1722, 

14 

22  W. 

1820, 

*24 

34  W. 

The  compass  is  used  for  setting  the  artificial  globe  north  and  south ;  but  care 
piust  be  taken  to  make  a  prpper  allowance  for  the  variation. 


35.  Latitude  of  a  Place,  on  the  terrestrial  globe,  is  its  dis- 
tance from  the  equator  in  degrees,  minutes  or  geographical  miles, 
and  is  reckoned  on  the  brass  meridian,  from  the  equator  to- 
wards the  north  or  south  pole. 


*  Edinburgh  Philosophical  Journal,  October  1820,  page  394. 


Chap,  I. 


DEFINITIONS,  &C, 


33 


3G.  Latitude  of  a  Star  or  Planet,  on  the  celestial  globe, 
is  its  distance  from  the  ecliptic,  northward  or  southward,  counted 
towards  the  pole  of  the  ecliptic,  on  the  quadrant  of  altitude.  The 
greatest  latitude  a  star  can  have  is  90  degrees,  and  the  greatest 
latitude  of  a  planet  is  nearly  8  degrees.*  The  sun  being  always 
in  the  ecliptic,  has  no  latitude. 

37.  The  Quadrant  of  Altitude  is  a  thin  flexible  piece  of 
brass  divided  upwards  from  0  to  90  degrees,  and  downwards 
from  0  to  18  degrees,  and  when  used  is  generally  screwed  to  the 
brass  meridian.  The  upper  divisions  are  used  to  determine  the 
distances  of  places  on  the  earth,  the  distances  of  the  celestial  bod- 
ies, their  altitudes,  &c.,  and  the  lower  divisions  are  applied  to  find- 
ing the  beginning,  end,  and  duration  of  twilight. 

38.  Longitude  of  a  Place,  on  the  terrestrial  globe,  is  the 
distance  of  the  meridian  of  that  place  from  the  first  meridian, 
reckoned  in  degrees  and  parts  of  a  degree  on  the  equator.  Lon- 
gitude is  either  eastward  or  westward,  according  as  the  place  is 
eastward  or  w^estward  of  the  first  meridian.  The  greatest  longi- 
tude that  a  place  can  have  is  180  degrees,  or  half  the  circumfer- 
ence of  the  globe. 

39.  Longitude  of  a  Star,  or  Planet,  is  reckoned  on  the 
ecliptic  from  the  point  Aries,  eastward,  round  the  celestial  globe. 
The  longitude  of  the  sun  is  what  is  called  the  sun's  place  on  the 
terrestrial  globe. 

40.  Almacantars,  or  parallels  of  altitude,  are  imaginary  cir- 
cles parallel  to  the  horizon,  and  serve  to  show  the  height  of  the 
sun,  moon,  or  stars.  These  circles  are  not  drav/n  on  the  globe, 
but  they  may  be  described  for  any  latitude  by  the  quadrant  of  al- 
titude. 

41.  Parallels  of  Celestial  Latitude  are  small  circles 
drawn  on  the  celestial  globe,  parallel  to  the  ecliptic. 

42.  Parallels  of  Declination  are  small  circles  parallel  to 
the  equinoctial  on  the  celestial  globe,  and  are  similar  to  the  par- 
allels of  latitude  on  the  terrestrial  globe. 

43.  Azimuth,  or  Vertical  Cjrcles,  are  imaginary  great  cir- 
cles passing  through  the  zenith  and  the  nadir,  cutting  the  horizon 
at  right  angles.  The  altitudes  of  the  heavenly  bodies  are  meas- 
ured on  these  circles,  which  circles  may  be  represented  by  screw- 
ing the  quadrant  of  altitude  on  the  zenith  of  any  place,  and  making 
the  other  end  move  along  the  wooden  horizon  of  the  globe. 


*  The  newly-discovered  planets,  or  Asteroids,  Ceres  aad  Pallas^  <^c.  do  not  ap- 
pear to  be  confined  within  this  limit. 


34 


DEFINITIONS,  &C. 


Parti. 


44.  The  Prime  Vertical  is  that  azimuth  circle  which  passes 
through  the  east  and  west  points  of  the  horizon,  and  is  always  at 
right  angles  to  the  brass  meridian,  which  may  be  considered  as 
another  vertical  circle  passing  through  the  north  and  south  points 
of  the  horizon. 

45.  The  Altitude  of  any  object  in  the  heavens  is  an  arc  of  a 
vertical  circle,  contained  between  the  centre  of  the  object  and  the 
hoi-izon.  When  the  object  is  upon  the  meridian,  this  arc  is  called 
the  meridian  altitude. 

46.  The  Zenith  Distance  of  any  celestial  object  is  the  arc  of 
a  vertical  circle,  contained  between  the  centre  of  that  object  and 
the  zenith ;  or  it  is  what  the  altitude  of  the  object  wants  of  90  de- 
grees. When  the  object  is  on  the  meridian,  this  arc  is  called  the 
meridian  zenith  distance. 

47.  The  Polar  Distance  of  any  celestial  object  is  an  arc  of  a 
meridian,  contained  between  the  centre  of  that  object  and  the  pole 
of  the  equinoctial. 

48.  The  Amplitude  of  any  object  in  the  heavens  is  an  arc  of 
the  horizon,  contained  between  the  centre  of  the  object  when  ris- 
ing, or  setting,  and  the  east  or  west  points  of  the  horizon.  Or,  it 
is  the  distance  which  the  sun  or  a  star  rises  from  the  east,  and  sets 
from  the  west,  and  is  used  to  find  the  variation  of  the  compass  at 
sea.  When  the  sun  has  north  declination,  it  rises  to  the  north 
of  the  east,  and  sets  to  the  north  of  the  west ;  and  when  it  has 
south  declination,  it  rises  to  the  south  of  the  east,  and  sets  to  the 
south  of  the  west.  At  the  time  of  the  equinoxes,  when  the  sun 
has  no  declination,  viz.  on  the  21st  of  March,  and  on  the  23d  of 
September,  it  rises  exactly  in  the  east,  and  sets  exactly  in  the 
west.* 

49.  The  Azimuth  of  any  object  in  the  heavens  is  an  arc  of  the 
horizon,  contained  between  a  vertical  circle  passing  through  the 
object,  and  the  north  or  south  points  of  the  horizon.  The  azi- 
muth of  the  sun,  at  any  particular  hour,  is  used  at  sea  for  finding 
the  variation  of  the  compass. 

50.  Hour  Circles,  or  Horary  Circles,  are  the  same  as  the 
meridians.    They  are  drawn  through  every  15  degreesf  of  the 


*  When  the  sun  is  in  the  equator  at  the  instant  of  rising,  he  does  not  rise  exactly 
due  east,  to  places  situated  in  north  or  south  latitude,  the  difference  being  greater 
as  the  latitude  increases  :  this  difference  is  still  greater  with  respect  to  the  moon. 

t  On  Cary^s  large  Globes  the  meridians  are  drawn  through  every  10  degrees,  as 
on  a  map. 


Chap,  I. 


DEFINITIONS,  &C. 


35 


equator,  each  answering  to  an  hour — consequently,  every  degree 
of  longitude  answers  to  four  minutes  of  time,  every  half  degree  to 
two  minutes,  and  every  quarter  of  a  degree  to  one  minute. 

On  the  globes  these  circles  are  supplied  by  the  brass  meridian, 
the  hour  circle  and  its  index. 

51.  The  Six  o'Clock  Hour  Line.  As  the  meridian  of  any 
place,  with  respect  to  the  sun,  is  called  the  12  o'clock  hour  circle; 
so  that  great  circle  passing  through  the  poles,  which  is  90  degrees 
distant  from  it  on  the  equator,  is  called  by  astronomers  the  six 
o'clock  hour  circle,  or  the  six  o'clock  hour  line.  The  sun  and  stars 
are  on  the  eastern  half  of  this  circle  six  hours  before  they  come 
to  the  meridian  ;  and  on  the  western  half  six  hours  after  they 
have  passed  the  meridian. 

52.  Culminating  Point  of  a  star  or  planet  is  that  point  of  its 
apparent  diurnal  path,  which,  on  any  given  day,  is  the  most  ele- 
vated. Hence  a  star  or  planet  is  said  to  culminate  when  it  comes 
to  the  meridian  of  any  place  ;  for  then  its  altitude  at  that  place  is 
the  greatest. 

53.  Apparent  Noon  is  the  time  when  the  sun  comes  to  the 
meridian  ;  viz.  12  o'clock,  as  shown  by  a  correct  sun-dial. 

54.  Mean  Noon,  12  o'clock,  as  shown  by  a  well  regulated 
clock,  adjusted  to  go  24  hours  in  a  mean  solar  day. 

55.  The  Equation  of  Time  at  noon  is  the  interval  between 
the  mean  and  apparent  noon,  viz.  it  is  the  difference  of  time  shown 
by  a  w^ell-regulated  clock  and  a  correct  sun-dial. 

56.  An  Apparent  Solar  Day  is  the  time  from  the  sun's  leav- 
ing the  meridian  of  any  place,  on  that  day,  till  it  returns  to  the 
same  meridian  on  the  next  day  ;  viz.  it  is  the  time  elapsed  from  12 
o'clock  at  noon,  on  any  day,  to  12  o'clock  at  noon  on  the  next 
day,  as  shown  by  a  correct  sun-dial.  An  apparent  solar  day  is 
subject  to  a  continual  variation,  arising  from  the  obliquity  of  the 
ecliptic,  and  the  unequal  motion  of  the  earth  in  its  orbit ;  the  du- 
ration, thereof  sometimes  exceeds,  at  others,  falls  short,  of  24  hours, 
and  the  difference  is  the  greatest  about  the  23d  of  December, 
when  the*  apparent  solaixday  is  30  seconds  more  than  24  hours, 
as  shown  by  a  well-regulated  clock. 

57.  A  Mean  Solar  Day  is  measured  by  equal  motion,  as  by  a 
clock  or  time-piece,  and  consists  of  24  hours.  There  are  in  the 
course  of  a  year  as  many  mean  solar  days  as  there  are  apparent 
solar  days,  the  slowness  of  the  sun  at  certain  seasons  being  com- 
pensated by  his  rapidity  at  others.  The  clock  is  faster  than  the 
sun-dial  from  the  24th  of  December  to  the  15th  of  April,  and  from 
the  16th  of  June  to  the  31st  of  August:  but  from  the  15th  of 
April  to  the  16th  of  June,  and  from  the  31st  of  August  to  the  24th 


36 


DErlNITIONS,  &C. 


Part  L 


of  December,  the  sun-dial  is  faster  than  the  clock.  From  the  2d 
of  November  to  the  11th  of  February,  the  apparent  solar  day  is 
greater  than  the  mean  solar  day  ;  from  the  11th  of  February  to 
the  15th  of  May,  the  apparent  solar  day  is  less  than  the  mean. 
From  the  15th  of  May  to  the  25th  of  July,  the  apparent  is  greater 
than  the  mean  ;  and  from  the  25th  of  July  to  the  2d  of  November 
the  apparent  is  less  than  the  mean.  On  February  11th,  May  15th, 
July  25th,  November  2d,  the  apparent  and  mean  solar  days  are  of 
equal  length.  The  greatest  interval  between  apparent  and  mean 
noon  happens  on  November  2d,  on  which  mean  noon  is  later  than 
apparent  noon  by  16  minutes  and  16  seconds ;  or,  which  amounts 
to  the  same  thing,  when  the  sun's  centre  transits  the  meridian  on 
November  2d,  the  time  shown  by  an  uniform  clock  is  11  hours, 
43  minutes,  44  seconds. 

58.  The  Astronomical  Day  is  reckoned  from  noon  to  noon, 
and  consists  of  24  hours.  This  is  called  a  natural  day,  being  of 
the  same  length  in  all  latitudes. 

59.  The  Artificial  Day  is  the  time  elapsed  between  the  sun's 
rising  and  setting,  and  is  variable  according  to  the  different  lati- 
tudes of  places. 

60.  The  Civil  Day,  like  the  astronomical  or  natural  day,  con- 
sists of  24  hours,  but  begins  differently  in  different  nations.  The 
ancient  Babylonians,  Pei-sians,  Syrians,  and  most  of  the  eastern 
nations,  began  their  day  at  sun-rising.  The  ancient  Athenians, 
the  Jews,  &c.  began  their  day  at  sun-setting,  which  custom  is  fol- 
lowed by  the  modern  Austrians,  Bohemians,  Silesians,  Italians, 
Chinese,  &c.  The  Arabians  begin  their  day  at  noon,  like  the 
modern  astronomers.  The  ancient  Egyptians,  Romans,  &c.  be- 
gan their  day  at  midnight,  and  this  method  is  followed  by  the 
English,  French,  Germans,  Dutch,  Spanish,  and  Portuguese. 

61.  A  SiDERiAL  Day  is  the  interval  of  time  from  the  passage 
of  any  fixed  star  over  the  meridian,  till  it  returns  to  it  again :  or, 
it  is  the  time  which  the  earth  takes  to  revolve  once  round  its  ax- 
is, and  consists  of  23  hours,  56  minutes,  4  seconds,  of  mean  solar 
time. 

In  elementary  books  of  astronomy  and  the  globes,  the  learner  is  generally 
told  that  the  earth  turns  on  its  axis  from  west  to  east  in  24  hours ;  but  the 
truth  is,  that  it  turns  on  its  axis  in  23  hours,  58  minutes,  4  seconds,  making  about 
366  revolutions  in  365  days,  or  a  year.  The  natural  day  would  always  consist 
of  23  hours,  56  minutes,  4  seconds,  instead  of  24  hours,  if  the  earth  had  no  other 
motion  than  that  on  its  axis ;  but  while  the  earth  has  revolved  eastward  once 
round  its  axis,  it  has  advanced  nearly  one  degree*  eastward  in  its  orbit.  To 


*  The  earth  goes  round  the  sun  in  365|  days  nearly ;  and  the  echptic,  which 
is  the  earth's  path  round  the  sun,  consists  of  360  degrees  j  hence  by  the  rule  of 


Chap.  I. 


DEFINITIONS,  &C. 


37 


illustrate  this,  suppose  the  sun  to  be  upon  any  particular  meridian  at  12  o'clock  on 
any  day  ;  in  23  hours,  56  minutes,  4  seconds,  afterwards,  the  earth  will  have  per- 
formed one  entire  revolution ;  but  it  will  at  the  same  time  have  advanced  nearly  one 
degree  eastward  in  its  orbit,  and  consequently  that  meridian  which  was  opposite  to 
the  sun  the  day  before,  will  be  now  one  degree  westward  of  it ;  therefore  the  earth 
must  perform  something  more  than  one  revolution  before  the  sun  appears  again  on 
the  same  meridian  ;  so  that  the  time  from  the  sun's  being  on  the  meridian  on  any 
day,  to  its  appearance  on  the  same  meridian  the  next  day,  is  24  hours. 

62.  A  Solar  Year,  or  tropical  year,  is  the  time  the  sun  takes 
in  passing  through  the  echptic,  from  one  tropic,  or  equinox,  till  it 
returns  to  it  again :  and  consists  of  365  days,  5  hours,  48  minutes, 
48  seconds. 

63.  A  SiDERiAL  Year  is  the  time  which  the  sun  takes  in  pas- 
sing from  any  fixed  star,  till  he  returns  to  it  again,  and  consists  of 
365  days,  6  hours,  9  minutes,  12  seconds  ;  the  siderial  year  is 
therefore  20  minutes,  24  seconds  longer  than  the  tropical  year, 
and  the  sun  returns  to  the  equinox  every  year  before  he  returns 
to  the  same  point  of  the  heavens  ;  consequently  the  equinoctial 
points  have  a  retrogade  motion. 

64.  The  Precession  of  the  Equinoxes,  arises  from  a  slow 
retrogade  motion  of  the  equinoctial  points  from  east  to  west,  con- 
trary to  the  order  of  the  signs,  which  is  from  west  to  east. 

This  motion,  from  the  best  observations,  is  about  50^*  seconds 
in  a  year,  so  that  it  would  require  25,791  yearsf  for  the  equinoctial 
points  to  perform  an  entire  revolution  westward  round  the  globe. 

In  the  time  of  Hipparchus,  and  the  oldest  astronomers,  the  equinoctial  points 
were  fixed  in  Aries  and  Libra  ;  but  the  signs  which  were  then  in  conjunction  with 
the  sun,  when  he  was  in  the  equinox,  are  now  a  whole  sign,  or  30  degrees  eastward 
of  it ;  so  that  Aries  is  now  in  Taurus,  Taurus  in  Gemini,  &c.  as  may  be  seen  on 
the  celestial  globe.  Hence  also  the  stars,  which  rose  and  set  at  any  particular 
season  of  the  year,  in  the  time  of  HesiodJ,  Eudoxus§,  Plinyl[,&c.  do  not  answer  to 
the  description  given  by  those  writers. 


three,  365^  D:  360  deg. :  :  ID:  69'  8^^  2,  the  daily  mean  motion  of  the  earth  in 
its  orbit,  or  the  apparent  mean  motion  of  the  sun  in  a  day.  Hence  a  clock,  or  chro- 
nometer, the  index  of  which  performs  an  exact  circuit  whilst  the  earth  (or  the  me- 
ridian of  an  observer)  moves  over  360 '  59'  8",  2,  is  said  to  be  adjusted  to  mean  solar 
time. 

*  In  Woodhouse^s  Astronomy,  the  mean  annual  precession  is  stated  to  be  5C.  34, 
and  in  the  new  French  Solar  Tables  50'.  1. 

t  For  the  circumference  of  the  equator  is  360  degrees,  and  50|":  1  year  :  :  360°: 
25,791  years. 

I  Hesiod  was  a  celebrated  Grecian  poet,  born  at  Ascra  in  Boeotia,  supposed  to 
have  flourished  in  the  time  of  Homer  ;  he  was  the  first  who  wrote  a  poem  on  Agri- 
culture, entitled  The  Works  and  the  Days,  in  which  he  introduces  the  rising  and  set- 
ting of  particular  stars,  &c.    Several  editions  of  his  work  are  now  extant. 

§  EuDOxus  was  a  great  geometrician  and  astronomer,  from  whom  Euclid,  the 
geometrician,  is  said  to  have  borrowed  great  part  of  his  elements  of  geometry. 
Eudoxus  was  born  at  Cnidus,  a  town  of  Caria,  in  Asia  Minor ;  he  flourished  about 
370  years  before  Christ. 

TT  Pliny,  generally  called  Pliny  the»Elder,  was  born  at  Verona,  in  Italy  j  he 


38 


DEFINITIONS,  &C. 


Part  I. 


65.  Positions  of  the  Sphere  are  three :  right,  parallel,  and 
oblique. 

66.  A  Right  Sphere  is  that  position  of  the  earth  where  the 
equinoctial  passes  through  the  zenith  and  the  nadir,  the  poles  being 
in  the  rational  horizon.  The  inhabitants  who  have  this  position 
of  the  sphere  live  at  the  equator :  it  is  called  a  right  sphere,  be- 
cause the  parallels  of  latitude  cut  the  horizon  at  right  angles.  In 
aright  sphere  the  parallels  of  latitude  are  divided  into  two  equal 
parts  by  the  horizon,  and  the  days  and  nights  are  of  equal  length. 

67.  A  Parallel  Sphere  is  that  position  the  earth  has  when 
the  rational  horizon  coincides  with  the  equator,  the  poles  being  in 
the  zenith  and  nadir.  The  inhabitants  who  have  this  position  of 
the  sphere,  (if  there  be  any  such  inhabitants)  live  at  the  poles  ;  it 
is  called  a  parallel  sphere,  because  all  the  parallels  of  latitude  are 
parallel  to  the  horizon.  In  a  parallel  sphere  the  sun  appears 
above  the  horizon  for  six  months  together,  and  he  is  below  the 
horizon  for  the  same  length  of  time. 

68.  An  Oblique  Sphere  is  that  position  the  earth  has  when 
the  rational  horizon  cuts  the  equator  obliquely,  and  hence  it  de- 
rives its  name.  All  inhabitants  on  the  face  of  the  earth,  (except 
those  who  live  exactly  at  the  poles  or  at  the  equator,)  have  this 
position  of  the  sphere.  The  days  and  nights  are  of  unequal 
lengths,  the  parallels  of  latitude  being  divided  into  unequal  parts 
by  the  rational  horizon. 

69.  Climate  is  a  part  of  the  surface  of  the  earth  contained  be- 
tween two  small  circles  parallel  to  the  equator,  and  of  such  a 
breadth,  that  the  longest  day  in  the  parallel  nearest  the  pole,  ex- 
ceeds the  longest  day  in  the  parallel  of  latitude  nearest  the  equa- 
tor, by  half  an  hour,  in  the  torrid  and  temperate  zones,  or  by  a 
month  in  the  frigid  zones  ;  so  that  there  are  24chmates  between 
the  equator  and  each  polar  circle,  and  six  climates  between  each 
polar  circle  and  its  pole. 

From  the  above  definition,  it  appears  that  all  places  situated  on  the  same  par- 
allel of  latitude  are  in  the  same  dimate  ;  but  we  must  not  infer  from  thence 
that  they  have  the  same  atmospherical  temperature  ;  large  tracts  of  uncultiva- 
ted lands,  sandy  deserts,  elevated  situations,  woods,  morasses,  lakes,  &c.  have  a 
considerable  effect  on  the  atmosphere.  For  instance,  in  Canada,  in  about  the 
latitude  of  Paris  and  the  south  of  England,  the  cold  is  so  excessive,  that  the 
greatest  rivers  are  frozen  over  from  December  to  April,  and  the  snow  commonly 


composed  a  work  on  natural  history  in  37  books  ;  it  treats  of  the  stars,  the  heavens, 
wind,  rain,  hail,  minerals,  trees,  flowers,  plants,  birds,  fishes,  and  beasts ;  besides  a 
geographical  description  of  every  place  on  the  globe,  &c.  &c.  Pliny  perished  by  an 
eruption  of  Vesuvius,  in  the  79th  year  of  Christ,  from  too  eager  curiosity  in  observ- 
ing the  phenomenon. 


Chap.  I. 


DEFINITIONS,  &:C. 


39 


lies  from  four  to  six  feet  deep.  The  Ancles  mountains,  though  part  of  them  are 
situated  under  the  torrid  zone,  are  at  the  summit  covered  with  snow,  which  cools 
the  air  in  the  adjacent  country.  The  heat  on  the  western  coast  of  Africa,  after  the 
wind  has  passed  over  the  sandy  desert,  is  almost  suffocating ;  whilst  the  same  wind 
having  passed  over  the  Atlantic  Ocean,  is  cool  and  pleasant  to  the  inhabitants  of 
the  Caribbean  Islands. 


I.  CLIMATES  between  the  Equator  and  the  Polar  Circles. 

Climate. 

Ends  in 
Latitude. 

Where 
the  long- 
est Day  is. 

Breadths 

of  the 
Climates. 

Climate. 

Ends  in 
Latitude. 

Where 
the  long- 
est Day  is. 

Breadths 
of  the 
Climate. 

I 

II 
III 
IV 
V 
VI 
VII 
VIII 
IX 
X 
XI 
XII 

D.  M. 

8  34 
16  44 
24  12 
30  48 
36  31 
41  24 

55  32 
49  2 
51  59 
54  30 

56  38 
58  27 

H.  M. 

12  30 

13  — 

13  30 

14  — 

14  30 

15  - 

15  30 

16  - 

16  30 

17  — 

17  30 

18  — 

D.  M. 

8  34 
8  10 
7  28 
6  36 
5  43 
4  53 
4  8 
3  30 
2  57 
2  31 
2  8 
1  49 

XIII 
XIV 
XV 
XVI 
XVII 
XVIII 
XIX 
XX 
XXI 
XXII 
XXIII 
XXIV 

D.  M. 

59  59 

61  18 

62  26 

63  22 

64  10 

64  50 

65  22 

65  48 

66  5 
66  21 
66  29 
66  32 

H  M. 

18  30 

19  — 

19  30 

20  — 

20  30 

21  — 

21  30 

22  — 

22  30 

23  — 

23  30 

24  — 

D.  M. 

1  32 
1  19 
1  8 

—  56 

—  48 

—  40 

—  32 

—  26 

—  17 

—  16 

—  8 

—  3 

11.  CLIMATES  between  the  Polar  Circles  and  the  Poles. 

Climate. 

Ends  in 
Latitude. 

Where 
the  long- 
est Day  is. 

Breadths 

of  the 
Climates. 

Climate. 

Ends  in 
Latitude. 

Where 
the  long- 
est Day  is. 

Breadths 

of  the 
Climates, 

XXV 
XXVI 
XXVII 

D.  M. 

67  18 
69  33 
73  6 

Da.  M. 

30  or  1 
60—2 
90—3 

D.  M. 

—  46 

2  15 

3  32 

XXVIII 
XXIX 
XXX 

D.  M. 

77  40 
82  59 
90  — 

Da.  M. 

120  or  4 
150  —  5 
180  —  6 

D.  M. 

4  35 

5  19 
7  1 

The  preceding  tables  may  be  constructed  by  the  globes,  as  will  be  shown  in  the 
problems,  but  not  with  that  exactness  given  above.  Tables  of  this  kind  are  gener- 
ally copied  from  one  author  into  another,  without  any  explanation  of  the  principles 
on  which  they  are  founded. 

Construction  of  the  first  Table. 

In  plate  IV.  figure  IV.  ho  represents  the  horizon,  m.<i  the  equator,  S  c  ^  a 
parrallel  of  the  sun's  greatest  dechnation,  no  the  elevation  of  the  pole  or  latitude 
of  the  place;  the  angle  c  ah  measured  by  the  arc  qo,  the  complement  of  the  lati- 
tude ;  a  6  is  the  ascensional  difference,  or  the  time  the  sun  rises  before  6  o'clock, 
and  6  c  the  sun's  dechnation.  Hence  by  Baron  Napier's  rules,  (see  Keith's  Spherical 
Trigonometry,)  rad.  X  sine  ah  —  cotangent  a*  {or  tangent  no)  X  tangent  b  c. 


40 


DEFINITIONS,  &C. 


Part  L 


VIZ.    Tangent  of  the  sun's  greatest  declination  23^  28''. 
Is  to  radius,  sine  of  90  degrees  ; 
Jls  sine  oj  the  ami's  ascensional  difference, 

Is  to  tangent  of  latitude.  A  general  rule. 

At  the  end  of  the  first  climate  the  sun  rises  ^  before  6  ;  and  in  every  climate,  if 
you  take  half  the  length  of  the  longest  day,  and  deduct  6  hours  therefrom,  the  re- 
mainder turned  into  degrees  will  give  the  ascensional  difference.  Hence  the 
ascensional  difference,  for  the  first  climate,  is  fifteen  minutes  of  time,  equal  to  3°  45'; 
for  the  second  chmate  30  minutes  =  7^  30' ;  for  the  third  cUmate  45  minutes  = 
11°  15' ;  for  the  fourth  chmate  1  hour  =  15°,  &c. 

Tangent  of  23°  28'  9.63761         Tangent  of  23°  8'  9.63761 

Is  to  radius,  sine  of  90°  10.00000  Is  to  radius,  sine  of  90°  10.00000 
As  sine  of  3°  45'.  8.81560         As  sine  of  7^  30'  9.11570 

Is  to  tang.  lat.  8°  34'        9.17799         Is  to  tang.  lat.  16°  44'  9.47809 

Constniction  of  the  Second  Table. 

The  longest  day  is  the  21st  of  June,  when  the  sun's  declination  is  23°  28'  north. 
Count  half  the  length  of  the  day  from  the  21st  June,  forward  and  backward  ;  find 
the  sun's  declination  answering  to  those  two  days  in  the  nautical  almanac,  or  in  a 
table  of  the  sun's  declination  ;  add  the  two  declinations  together,  and  divide  their 
sum  by  2,  substract  the  quotient  from  90  degrees,  and  the  remainder  is  the  latitude. 
As  the  sun's  declination  is  variable,  it  ought  to  be  taken  out  of  the  almanac,  or 
tables,  for  leap  year  and  the  three  following  years,  a  mean  of  these  declinations, 
used  as  above,  will  give  the  latitude  as  correct  as  the  nature  of  the  problem  admits 
of,  and  in  this  manner  the  second  table  was  constructed.  Riccioli,  (an  Italian 
astronotwer  and  mathematician,  born  at  Ferrara,  in  the  Pope's  dominions,  1598,)  in 
his  Jlstronomioi  Reformaice,  published  in  1665,  makes  an  allowance  for  the  refraction 
of  the  atmosphere  in  a  table  of  climates.  He  considers  the  increase  of  days  to  be 
by  half  hours,  from  12  to  16  hours;  by  hours,  from  16  to  20  hours;  by  2  hours, 
from  20  to  24  hours ;  and  by  months  in  the  frigid  zones,  making  the  number  of  the 
days  of  each  month  in  the  north  frigid  zone  something  more  than  those  in  the 
south ;  but  as  the  refraction  of  the  atmosphere  is  so  extremely  variable,  that  scarce- 
ly any  two  mathematicians  agree  with  respect  to  the  quantity,  it  is  evident  that  a 
table  of  climates,  calculated  with  such  an  uncertain  allowance,  can  be  of  no  ma- 
terial advantage. 

70.  A  Zone  is  a  portion  of  the  surface  of  the  earth  contained 
between  two  small  circles  parallel  to  the  equator,  and  is  similar 
to  the  term  climate,  for  pointing  out  the  situations  of  places  on 
the  earth,  but  less  exact ;  as  there  are  only^re  zones,  which  have 
been  distinguished  by  particular  names ;  whereas  there  are  60 
climates. 

71.  The  Torrid  Zone  extends  from  the  tropic  of  Cancer  to 
the  tropic  of  Capricorn,  and  is  46l56'  broad.  This  zone  was 
thought  by  the  ancients  to  be  uninhabited,  because  it  is  contin- 
ually exposed  to  the  direct  rays  of  the  sun ;  and  such  parts  of 
the  torrid  zone  as  were  known  to  them  w^ere  sandy  deserts;  as, 
the  middle  of  Africa,  Arabia,  &c. ;  and  those  sandy  deserts  which 
extend  beyond  the  left  bank  of  the  Indus,  toward  Agimere. 

72.  The  Two  Temperate  Zones.  The  north  temperate  zone 
extends  from  the  tropic  of  Cancer  to  the  arctic  circle ;  and  the 
south  temperate  zone  from  the  tropic  of  Capricorn  to  the  ant  arc- 


Chap,  I. 


DEFINITIONS,  &C. 


41 


tic  circle.  These  zones  are  each  43^'  broad,  and  were  called 
temperate  by  the  ancients,  because  meeting  the  sun's  rays  ob- 
liquely, they  enjoy  a  moderate  degree  of  heat. 

73.  The  Two  Frigid  Zones.  The  north  frigid  zone,  or  ratlier 
segment  of  the  sphere,  is  bounded  by  the  arctic  circle.  The  north 
pole,  which  is  23°  28'  from  the  arctic  circle,  is  situated  in  the  cen- 
tre of  this  zone.  The  south  frigid  zone  is  bounded  by  the  antarc- 
tic circle,  distant  23°  28  from  the  south  pole,  which  is  situated  in 
the  centre  of  this  zone. 

74.  Amphiscii  are  the  inhabitants  of  the  torrid  zone  ;  so  called, 
because  their  shadows  fall  north  or  south  at  different  times  of  the 
year ;  the  sun  being  sometimes  to  the  south  of  them  at  noon,  and 
at  other  times  to  the  north.  When  the  sun  is  vertical,  or  in  the 
zenith,  which  happens  twice  in  the  year,  the  inhabitants  have  no 
shadow,  and  are  then  called  Ascii,  or  sliadowless. 

75.  Heteroscii  is  a  name  given  to  the  inhabitants  of  the  tem- 
perate zones,  because  their  shadows  at  noon  fall  only  one  way. 
Thus,  the  shadow  of  an  inhabitant  of  the  north  temperate  zone 
always  falls  to  the  north  at  noon,  because  the  sun  is  then  due 
south ;  and  the  shadow  of  an  inhabitant  of  the  south  temperate 
zone  falls  towards  the  south  at  noon,  because  the  sun  is  due  north 
at  that 'time. 

76.  Periscii  are  those  people  who  inhabit  the  frigid  zones,  so 
called,  because  their  shadows,  during  a  revolution  of  the  earth  on 
its  axis,  are  directed  towards  every  point  of  the  compass.  In  the 
frigid  zones  the  sun  does  not  set  during  several  revolutions  of  the 
earth  on  its  axis. 

77.  Antgeci  are  those  who  live  in  the  same  degree  of  longitude, 
and  in  equal  degrees  of  latitude,  but  the  one  in  north  and  the  other 
in  south  latitude.  They  have  noon  at  the  same  time,  but  contrary 
seasons  of  the  year ;  consequently  the  length  of  the  days  to  the 
one,  is  equal  to  the  length  of  the  nights  to  the  other.  Those  who 
live  at  the  equator  can  have  no  Antoeci. 

78.  Periceci  are  those  who  live  in  the  same  latitude,  but  in  op- 
posite longitudes ;  when  it  is  noon  with  the  one,  it  is  midnight 
with  the  other ;  they  have  the  same  length  of  days,  and  the  same 
seasons  of  the  year.  The  inhabitants  of  the  poles  can  have  no 
Perioeci. 

79.  Antipodes  are  those  inhabitants  of  the  earth  who  live  di- 
ametrically opposite  to  each  other,  and  consequently  walk  feet  to 
feet ;  their  latitudes,  longitudes,  seasons  of  the  year,  days  and 
nights,  are  all  contrary  to  each  other. 

80.  The  Right  Ascension  of  the  sun,  or  of  a  star,  is  that  de- 
gree of  the  equinoctial  which  rises  with  the  sun,  or  star,  in  a  right 

6 


42 


DEFINITIONS,  &C. 


Part  I. 


sphere,  and  is  reckoned  from  the  equinoctial  point  Aries  eastward 
round  the  globe. 

81.  Oblique  Ascension  of  the  sun,  or  of  a  star,  is  that  degree 
of  the  equinoctial  which  rises  with  the  sun  or  star,  in  an  oblique 
sphere,  and  is  likewise  counted  from  the  point  Aries  eastward 
round  the  globe. 

82.  Oblique  Descension  of  the  sun,  or  of  a  star,  is  that  degree  of 
the  equinoctial  which  sets  with  the  sun  or  star  in  an  oblique  sphere. 

83.  The  Ascensional  or  Descensional  Difference  is  the 
difference  between  the  right  and  oblique  ascension,  or  the  differ- 
ence between  the  right  and  oblique  descension,  and,  with  respect 
to  the  sun,  it  is  the  time  he  rises  before  6  in  the  spring  and  sum- 
mer, or  sets  before  6  in  the  autumn  and  winter. 

84.  The  Crepusculum,  or  Twilight,  is  that  faint  light  which 
we  perceive  before  the  sun  rises,  and  after  he  sets.  It  is  produced 
by  the  rays  of  light  being  refracted  in  their  passage  through  the 
earth's  atmosphere,  and  reflected  from  the  different  particles 
thereof.  The  twihght  is  supposed  to  end  in  the  evening  when 
the  sun  is  18  degrees  below  the  horizon,  or  when  stars  of  the  sixth 
magnitude  (the  smallest  that  are  visible  to  the  naked  eye)  begin 
to  appear ;  and  the  twilight  is  said  to  begin  in  the  morning,  or  it 
is  day-hreali,  when  the  sun  is  again  within  18  degrees  of  the  hori- 
zon. The  twilight  is  the  shortest  at  the  equator,  and  longest  at 
the  poles  ;  here  the  sun  is  near  two  months  before  he  retreats  18 
degrees  below  the  horizon,  or  to  the  point  where  his  rays  are  first 
admitted  into  the  atmosphere  ;  and  he  is  only  two  months  more 
before  he  arrives  at  the  same  parallel  of  latitude. 

85.  Refraction.  The  earth  is  surrounded  by  a  body  of  air, 
called  the  Atmosphere,  through  which  the  rays  of  light  come  to  the 
eye  from  all  the  heavenly  bodies  ;  and  since  these  rays  are  admit- 
ted through  a  vacumn^ov  at  least  through  a  very  rare  medium*,  and 
fall  obliquely  upon  the  atmosphere,  which  is  a  dense  medium,  they 
will,  by  the  laws  of  optics,  be  refracted  in  lines  approaching  near- 
er to  a  perpendicular  from  the  place  of  the  observer  (or  nearer  to 
the  zenith)  than  they  would  be  were  the  medium  to  be  removed. 
Hence  all  the  heavenly  bodies  appear  higher  than  they  really  are, 
and  the  nearer  they  are  to  the  horizon  the  greater  the  refraction, 
or  difference  between  their  apparent  and  true  altitudes,  will  be ;  at 
noon  the  refraction  is  the  least.  The  sun  and  the  moon  appear  of 
an  oval  figure  sometimes  near  the  horizon,  by  reason  of  refraction ; 


*  Any  fluid  or  substance  through  which  a  ray  of  hght  can  penetrate,  is  called  a 
medium,  as  air,  water,  oil,  glass,  &c.  The  air  near  the  surface  of  the  earth  is  more 
dense  than  in  the  higher  regions  of  the  atmosphere  ;  and  beyond  the  atmosphere, 
the  rays  of  light  are  supposed  to  meet  with  little  or  no  resistance. 


Chap.  I. 


DEFINITIONS,  &C. 


43 


for  the  under  side  being  more  refracted  than  the  upper,  the  per- 
pendicular diameter  will  be  less  than  the  horizontal  one,  which  is 
not  affected  by  refraction. 


It  has  long  been  established,  by  experiment,  that  a  ray  of  light  passing  from  a 
rarer  to  a  denser  medium,  is  refracted  towards  the  denser  medium.  Thus,  if  abc 
be  the  boundary  between  two  media,  of  which  the  lower  one  is  the  denser,  then  a 
ray  of  light  sb,  instead  of  pursuing  its  direction  ssw,  is  deflected  in  the  direction  be, 
and  a  star,  instead  of  appearing  at  s,  would  appear  at  e,  that  is  nearer  to  a  perpen- 
dicular BP,  meeting  a  tangent  at  the  point  of  incidence  b.  Again,  if  def  be  a 
similar  boundary,  separating  the  rarer  medium  contained  between  abc  and  def 
from  the  denser  medium  contained  between  def  and  ghi,  the  ray  of  light  instead  of 
pursuing  its  new  course  BEn  will  be  again  deflected  in  the  direction  eh  ;  and  similar 
effects  will  be  produced  if  more  media  and  their  boundaries  be  added.  Hence,  a 
ray  of  light,  instead  of  being  a  continued  straight  hne,  is  broken  into  parts  be,  eh, 
HL,  inchned  to  each  other  at  the  angles,  beh,  ehl,  &c.  If  we  suppose  these  media 
to  be  indefinitely  increased,  and  their  boundaries  to  approach  each  other  by  spaces 
extremely  smaH,  the  parts  be,  eh,  hl,  may  be  considered  as  curviHnear,  and  the 
course  of  a  ray,  instead  of  being  polygonal,  will  be  a  curve,  concave  towards  the  den- 
ser medium.    This  may  be  more  adequately  represented  by  the  following  figure. 

Here  the  media  are  no  longer  par- 
celled out  into  diflTerent  strata  of  va- 
riable density,  but  are  considered  as 
one  medium  of  a  density  continually 
varying  ;  such  is  the  earth's  atmos- 
phere, the  most  dense  at  its  surface, 
and  decreasing  towards  the  higher 
regions.  A  ray  of  hght  will  conse- 
quently, in  its  passage  through  the 
atmosphere,  be  deflected  into  a  curve 
concave  towards  the  earth's  surface, 
and  will  enter  a  spectator's  eye  in 
the  direction  of  a  tangent  to  that 
curve  J  a  star  will,  therefore  appear  in  that  direction. 


44 


DEFINITIONS,  &€. 


Part  1. 


Let  o  be  the  place  of  an  observer,  hor  his  horizon,  and  s  a  star  ;  aod  a  section  of 
the  earth,  formed  by  a  vertical  plane  passing  through  the  star  at  s  and  the  centre 
(c)  of  the  earth.  Here  e  is  the  apparent  place  of  the  star,  and  s  its  true  place  ; 
the  angle  cor  is  the  apparent  altitude  of  the  star,  and  the  angle  sor  its  true  alti- 
tude, the  angle  eos,  therefore  is  the  refraction.  If  the  star  were  at  z,  the  zenith  of 
the  observer,  its  height  would  suffer  no  refraction.  Refraction  depends  upon  a 
star's  altitude  and  the  heights  of  the  barometer  and  thermometer  ;  viz.  upon  the 
height  of  the  object,  and  the  state  of  the  atmosphere  ;  hence  we  sometimes  are  able 
to  see  the  tops  of  mountains,  towers,  or  spires  of  churches,  which  at  other  times 
are  invisible,  though  we  stand  in  the  same  place.  The  ancients  knew  nothing  of 
refraction,  the  first  who  composed  a  table  thereof  was  Tycho  Brake.  The  table 
now  in  common  use  was  constructed  by  Dr.  Bradley*,  or  from  his  formula,  being 
the  result  of  many  trials,  conjectures,  and  experiments.  In  the  Nautical  Almanac 
for  1822,  there  is  a  table  of  refractions,  calculated  from  an  ingenious  formula,  ex- 
plained by  Dr.  Young,  in  the  Philosophical  Transactions  for  1819. 

The  sun's  meridian  altitude  on  the  longest  day  decreases  from  the  tropic  of  Cancer 
to  the  north  pole;  and  in  the  torrid  zone,  when  the  sun  is  vertical  there  is  no  re- 
fraction ;  hence  the  refraction  is  the  least  in  the  torrid  zone,  and  greatest  at  the 
poles.  Varenius,  in  his  geography,  speaking  of  the  wintering  of  the  Dutch  in  Nova 
Zembla,  latitude  76°  north,  in  the  year  1596,  says  they  saw  the  sun  in  the  year  1597 
six  days  sooner  than  they  would  have  seen  him,  had  there  been  no  refraction. 

86.  Parallax.  That  part  of  the  heavens  in  which  a  planet 
would  appear,  if  viewed  from  the  surface  of  the  earth,  is  called 
its  apparent  place ;  and  the  point  in  which  it  would  be  seen  at  the 
same  instant  from  the  centre  of  the  earth  is  called  its  true  place  ; 
the  difference  is  the  parallax.  A  fixed  star,  on  account  of  its  great 
distance  from  the  earth,  has  no  sensible  parallax. 

Let  c  be  the  centre  of  the  earth,  o  the 
place  of  an  observer  on  its  surface  whose 
sensible  horizon  is  hor,  and  zenith  z.  Then 
if  znmR  be  a  portion  of  a  vertical  circle  in 
the  heavens,  and  s  the  real  place  of  any  ob- 
ject in  the  horizon,  if  cs  be  joined  and  pro- 
duced to  m,  it  will  show  Ihe  true  place  of  s  ; 
the  angle  msR  or  cso  is  the  parallax.  Hence 
the  altitudes  of  the  celestial  bodies  are  de- 
pressed by  parallax,  which  is  the  greatest 
at  the  horizon,  and  decreases  as  the  altitude 
of  the  object  increases  ;  for  the  angle  cot)  is 
greater  than  the  angle  cos,  consequently  the  angle  ot;c  is  less  than  the  angle  osc. 
At  the  zenith  z  the  angle  ovc  vanishes,  and  therefore  the  parallax  ceases. 

87.  Angle  of  Position  between  two  places  on  the  terrestrial 
globe,  is  an  angle  at  the  zenith  of  one  of  the  places  ;  formed  by  the 
meridian  of  that  place,  and  a  vertical  circle  passing  through  the 


*  The  third  astronomer  royal :  he  died  in  the  year  1762. 


Chap.  I. 


DEFINITIONS,  (fec. 


45 


other  place,  being  measured  on  the  horizon  from  the  elevated 
pole  towards  the  vertical  circle. 

The  Angle  op  position  op  a  star,  is  an  angle  formed  by  two  great  circles 
intersecting  each  other  in  the  place  of  the  star,  the  one  passing  through  the  pole  of 
the  equinoctial,  the  other  through  the  pole  of  the  ecliptic.  This  angle  may  be 
computed  from  the  obliquity  of  the  ecliptic,  and  the  co-latitude  and  co-declination 
of  the  star  ;  it  is  used  in  several  astronomical  calculations.  M.  Lalande  has  given 
a  table  of  the  angles  of  positions  of  stars  in  his  Astronomy,  2d  ed.  vol.  i.  page  488. ; 
and  in  the  Cotmaissance  des  Terns  for  1804,  there  is  a  table  of  the  same  kind. 

88.  Rhumbs  are  the  divisions  of  the  horizon  into  32  part^^ 
called  the  points  of  the  compass.  The*  ancients  were  acquainted 
only  with  the  four  cardinal  points,  and  the  wind  was  said  to  blow 
from  that  point  to  which  it  was  nearest. 

A  Rhumb  line  geometrically  speaking,  is  a  loxodromic  or  spiral  curve,  drawn, 
or  supposed  to  be  drawn,  upon  the  earth,  so  as  to  cut  each  meridian  at  the  same 
angle,  called  the  proper  angle  of  the  rhumb.  If  this  line  be  continued,  it  will 
never  return  into  itself  so  as  to  form  a  circle,  except  it  happens  to  be  due  east  and 
west,  or  due  north  and  south ;  and  it  can  never  be  a  straight  line  upon  any  map, 
except  the  meridians  be  parrallel  to  each  other,  as  in  Mercator's  and  the  plane 
chart.  Hence  the  difficulty  of  finding  the  true  bearing  between  two  places  on  the 
terrestrial  globe,  or  on  any  map  but  4hose  above  mentioned.  The  bearing  found 
by  a  quadrant  of  altitude  on  a  globe,  is  only  the  measure  of  a  spherical  angle  upon 
the  surface  of  that  globe,  as  defined  by  the  angle  of  position,  and  not  the  real  beao-* 
ing  or  rhumb,  as  shown  by  the  compass ;  for,  by  the  compass,  if  a  place  a  bear  due 
east  from  a  place  b,  the  place  b  will  bear  due  west  from  the  place  a  ;  but  this  is  not 
the  case  when  measured  with  a  quadrant  of  altitude. 

89.  The  Fixed  Stars  are  so  called  because  they  have  usually 
been  observed  to  keep  the  same  distance  with  respect  to  each 
other.  The  stars  have  an  apparent  motion  from  east  to  west,  in 
circles  parrallel  to  the  equinoctial,  arising  from  the  revolution  of 
the  earth  on  its  axis,  from  west  to  east ;  and,  on  accout  of  the 
precession  of  the  equinoxes,  their  longitudes  increase  about  50  1-4 
seconds  in  a  year ;  this  likewise  causes  a  variation  in  their  decli-^ 
nations  and  right  ascensions :  their  latitudes  are  also  subject  to  a 
small  variation. 

90.  The  Poetical  Rising  and  Setting  of  the  Stars,  so 
called  because  they  are  taken  notice  of  by  the  ancient  poets,  who 
referred  the  rising  and  setting  of  the  stars  to  the  sun.  Thus, 
when  a  star  rose  with  the  sun,  or  set  when  the  sun  rose,  it  was 
said  to  rise  and  set  Cosmically.  When  a  star  rose  at  sun-setting, 
or  set  with  the  sun,  it  was  said  to  rise  and  set  Acronically. 
When  a  star  first  became  visible  in  the  morning,  after  having  been 
so  near  the  sun  as  to  be  hid  by  the  splendor  of  his  rays,  it  was 


*  Phny's  Nat.  Hist.  Lib.  II.  chap.  47. 


46 


DEFINITIONS,  &C. 


Part  I. 


said  to  Rise  Helically  ;  and  when  a  star  first  became  invisible 
in  the  evening,  on  account  of  its  nearness  to  the  sun,  it  vsras  said 
i  to  Set  Helically. 

91.  A  Constellation  is  an  assemblage  of  stars  on  the  surface 
of  the  celestial  globe,  circumscribed  by  the  outlines  of  some  as- 
sumed figure,  as  a  ram,  a  dragon,  a  hear,  &c.  This  division  of 
the  stars  into  constellations  is  necessary,  in  order  to  direct  a  per- 
son to  any  part  of  the  heavens  vi^here  a  particular  star  is  situated. 

The  following  tables  contain  all  the  constellations  on  the  British  Globes.  The 
ZODIACAL  constellations  are  12  in  number,  the  northern  constellations  35,  and 
the  SOUTHERN  47,  making  in  the  whole  94.  By  adding  together  the  numbers  of 
stars  in  ih.e  first  columns  of  the  following  tables,  the  total  will  be  found  to  be  3457 ; 
of  this  number  there  are  only  19  of  the  first  magnitude,  and  422  cannot  be  seen  at 
London.  The  largest  stars  are  called  stars  of  the  first  magnitude.  Those  of  the 
sixth  magnitude  are  the  smallest  that  can  be  seen  by  the  naked  eye.  The  figures 
on  the  left  hand  of  the  tables  show  the  number  of  stars  in  each  constellation,  from 
Flamsteacfs  Catalogue  ;  R  denotes  right  ascension,  D  declination  of  the  middle  of 
the  several  constellations,  for  the  ready  finding  them  on  the  globe.  The  modern 
constellations  are  distinguished  from  the  ancient  by  an  asterisk. 

I.  Constellations  in  the  Zodiac. 

«^  ^  J^ames  of  the  Constellations,  and  of  the  principal  Stars 

t>2  S  in  each,  with  their  magnitudes. 

66.  Aries,  The  Ram,  Arietis  2,       .  . 
141.  Taurus,  The  Bull,  Aldebaran  1,  the  Pleiades,  the  Hyades, 

85.  Gemini,  The  Twins,  Castor  1,  Pollux  2, 

83.  Cancer,  The  Crab,  Acubene  4, 

95.  Leo,  The  Lion,  Regulus  or  Cor  Leonis  1,  Deneb  2, 
110.  Virgo,  The  Virgin,  Spica  Virginis  1,  Vendemiatrix  2, 

51.  Libra,  The  Balance,  Zubenich  Meli  2, 

44.  Scorpio,  The  Scorpion,  Antares  1, 

69.  Sagittarius,  The  Archer, 

51.  Capricorn  us,  The  Goat, 
108,  Aquarius,  The  Water  Bearer,  Scheat  3, 
il3.  Pisces,  The  Fishes,  .  .  . 


R.  D. 

30.  22  N. 

65.  16  N. 

111.  32  N. 

128.  20  N. 

150.  15  N. 

192.  5  N. 

226.  8  S. 

244.  26  S. 

285.  35  S. 

310.  20  S. 

335.  4  S. 

5.  10  N. 


II.  The  Northern  Constellations. 


66.  Andromeda,  Mirach  2,  Almaach  2,                 .  .  15.  35  N. 

71.  Aquila,  TAe  EagZe,  with  Antinous,  Altair  or  Atair,  1,  .  295.  8  N. 

25.  Asterion  et  Chara*,  vel  Canes  Venatici,  The  Greyhounds,  200.  40  N. 

66.  Auriga,  The  Charioteer  or  Waggoner,  Capella  1,  ,        .  75.  45  N. 

54.  Bootes,  Arcturus  1,  Mirach  3,                        .  .  212.  20  N. 

58.  Camelopardalus*,  The  Comelopard,                  .  ,  68.  70  N. 

59.  Ca-iput  Medusse,  The  Head  of  Medusa,  and  Ferseus,  .  44.  40  N. 

55.  Cassiopeia,  The  Lady  in  her  Chair,  Schedar  3,  12.  60  N. 
35.  Cepheus,  Alderamin  3,  ...  338.  65  N. 
—  Cerberus,  The  Three-headed  Dog,  and  Hercules,  .  271.  22  N. 
43.  Coma  Berenices,  Berenice's  Hair,  .  185.  26  N. 

3.  Cor  Caroli*,  Charles  Heart,                            .  .  191.  39  N. 

21.  Corona  Borealis,  The  JsTorthern  Crown,  Alphacca  2,  235.  30  N. 

81.  Cygnus,  The  Swan,  Deneb  Adige  1,  .  308.  42  N. 


Chap.  I. 


DEFINITIONS, 


47 


^1 


jSTames  of  the  Constellations  and  of  the  principal  Stars 
in  each,  with  their  magnitudes. 


R. 

D. 

308. 

15  N. 

270. 

66  N. 

316. 

5  N. 

245. 

22  N. 

336. 

43  N. 

150. 

35  N. 

111. 

50  N. 

283. 

38  N. 

225. 

5  N. 

40. 

27  N. 

340. 

14  N. 

46. 

49  N. 

295. 

18  N. 

275. 

10  S. 

235. 

10  N. 

260. 

13  N. 

275. 

7  N. 

27. 

32  N. 

31. 

29  N. 

153. 

60  N. 

235. 

75  N. 

300. 

25  N. 

30. 

75  N. 

18.  Delphinus,  The  Dolphin, 
80.  Draco,  The  Dragon,  Rastaben  2 

10.  Equulus,  The  Little  Horse, 
113.  Hercules,  virfe  Cerberus,  Ras  Algethi  3, 

16.  Lacerta*,  The  Lizard,  .  . 

53.  Leo  Minor*,  The  Little  Lion, 
44.  Lynx*,  The  Lynx,  . 
22.  Lyra,  The  Harp,  Vega  or  Wega  1. 

11.  Mons  Moenalus  The  Mountain  Mmnalus, 

6.  Musca*,  The  Fly, 
89.  Pegasus,  The  Flying  Horse,  Markab  2,  Scheat  1, 

Perseus,  vide  Caput  Medusa,  Algenib  2,  Algol  2, 

18.  Sagitta,  The  Arrow, 

8.  Scutum  Sobieski*  SobieskVs  Shield, 
64.  Serpens,  The  Serpent, 

74.  Serpentarius,  The  Serpent  Bearer,  Ras  Alhagus  2, 

7.  Taurus  Poniatowski*,  The  Bull  of  Poniatowski, 
11.  Triangulum,  The  Triangle, 

5.  Triangulum  Minus,  The  Little  Triangle, 
87.  Ursa  Major,  The  Great  Bear,  Dubhe  1,  Alioth  2,  Benetnach  2, 
24.  Ursa  Minor,  The  Little  Bear,  Polar  Star,  or  Alrukabah  2, 
37.  Vulpecula  et  Anser*,  The  Fox  and  Goose, 

W.  Tan-audus*,  The  Rein  Deer,  .  .  , 

To  the  preceding  list  of  northern  constellations,  foreign  Mathematicians  have 
added  Le 'Messier,  Taurus  Regalis,  Fredericks  Ehre,  Frederick's  Glory,  Tubus 
Herschelii  Major,  HerscheVs  Great  Telescope. 

III.  The  Southern  Constellations. 

11.  Apus  vel  Avis  Indica*,  The  Bird  of  Paradise,     .  .  252. 

9.  Ara,  The  Altar,  .  .  255. 
64.  Argo  Navis,  The  Ship  Argo,  C«nopus  1,  .115. 

3.  Brandenburgium  Sceptrum*,  The  Sceptre  of  Brandenburg,  67. 
31.  Canis  Major,  TAe  Greoi  Dog-,  Sirius  1,  .  .  105. 
14.  Canis  Minor,  The  Little  Dog,  Procyon  1,  110. 
35.  Centaurus,  The  Centaur,  .  .  200. 
97.  Cetus,  The  Whale,  Mencar  2,  .  .  •  25. 
10.  Chamseleon*,  The  Cameleon,  .  175. 

4.  Circinus*,  The  Compasses,  .  .  222. 
10.  Columba  Noachi*,  Mah's  Dove,  .  85. 

12.  Corona  Australis,  The  Southern  Crown,  .  278. 
9.  Corvus,  The  Crow,  Algorab  3,  ,                .  185. 

31.  Crater,  The  Cup  or  Goblet,  Alkes  3,  .               .  168. 

6.  Crux*,  The  Cross,                            .  ?  .183. 

7.  Dordido  or 'KiphisiS*,  The  Sword  Fish,  •  75. 

8.  Equuleus  Pictorius*,  The  Painter^ s  Easel,  .  84. 
84.  Eridanus,  The  River  Po,  Acherner  1,  .  .  60. 
14.  Fornax  Chemica*,  The  Furnace,  .  42. 

13.  Grus*,  The  Crane,  .  .  .  330. 
12.  Horologium*,  The  Clock,  .  40. 
60.  Hydra,  The  Water  Serpent,  Cor  Hydrse  1,  .  139. 
10.  Hydrus*,  The  Water  Snake,  .  .  28. 
12.  Indus*,  The  Indian,  .          .  .315. 

19.  Lepus,  T/ieHare,  .  .  80. 
24.  Lupus,  The  Wolf,       .  .                         .  230. 

3.  Machina  Pneumatica*,  TAc  ./3iV  Fwrnp,  .  150. 

10.  Microscopium*.  The  Microscope,  .         .  .315. 

31,  Monoceros*,  The  Unicorn,  -  H^- 


75  S. 
55  S. 
50  S. 
15  S. 
20  S. 

5N. 
50  S. 
12  S. 
78  S. 

u  s. 

35  S. 
40  S. 
15  S. 
15  S. 
60  S. 
62  S. 
55  S. 

10  s. 
30  S. 
45  S. 
60  S. 

8  S. 
68  S. 
65  S. 
18  S. 
45  S. 
32  S. 
35  S. 

0 


Definitions,  <^c. 


Part  1. 


^  JVames  of  the  Constellations,  and  of  the  princi'pal  Stars 

Cc  i  in  each,  with  their  magnitudes. 

^  5- 

30.  Mons  Mensae*,  The  Table  Mountain, 
4.  Musca  Australis,  vel  Apes*,  The  Southern  Fly  or  Bee, 
12.  Norma  vel  Gluadra  Kuclidis*,  Euclid's  Square, 
43.  Octans  Hadleianus*,  Hadley^s  Octant, 

12.  Officina  Sculptoria*,  The  Sculptors  Shop, 
78.  Orion,  Betelgeux  1,  Rigel  1,  Bellatrix  2, 
14.  Pavo*,  The  Peacock, 

13.  Phajnix*, 

24.  Piscis  Notius,  vel  Australis,  The  Southern  Fish,  Fomalhaut  1, 

8.  Piscis  Volans*,  The  Fhjing  Fish, 

16.  Praxiteles,  vel  cela  Sculptoria*,  The  Engraver's  Tools, 

4.  Pyxis  Nautica*,  The  Mariner's  Compass, 
10.  Reticulus  Rhomboidalis*,  T/ie  J2/jom6oic^aZ  JVef, 
12.  Robur  Caroli*,  Charle's  Oak, 
41.  Sextans*,  The  Sextant, 

9.  Telescopium*,  The  Telescope, 

9.  Touchan*,  The  American  Goose,  .  : 

5.  Triangulum  Australis",  The  Southern  Triangle, 
—  Xiphias*,  vide  Dorado,  .  .  . 

Foreign  mathematicians  have  added  to  the  preceding  list  of  southern  constella- 
tions, Solitaire,  an  Indian  Bird;  Psalterium  Georgianum,  The  Georgian  Psaltery ; 
Tubus  Herschelii  Minor,  ifersc/id's  Less  Telescope;  Montgolfier's  Balloon;  The 
Press  of  Guttenberg  ;  and  the  Cat. 


■p 

U. 

/o. 

li  b. 

J  SO. 

f  Q  C< 

bo  fc). 

45  to. 

9  1  n 
o  1 U. 

oU  to. 

Q 

o. 

oa  to. 

QA 

oU. 

n 

OXJi. 

bo  to. 

lU. 

KA  Q. 

OU  to 

OOO. 

OA  CJ 
OU  to. 

bo  io. 

68. 

40  S. 

130. 

30  S. 

62. 

62  S. 

159. 

50  S. 

145. 

0 

278. 

50  S. 

359. 

66  S. 

238. 

65  S. 

75. 

62  S. 

"EiXplanalim,  of  the  different  emblematical  Figures  delineated  on  the  Surface  of  the 
Celestial  Globe. 

I.  THE  CONSTELLATIONS  IN  THE  ZODIAC. 

It  is  conjectured  that  the  figures  in  the  siggm  of  the  zodiac  are  descriptive  of  the 
seasons  of  the  year,  and  that  they  are  Chaldean  or  Egyptian  hieroglyphics,  intend- 
ed to  represent  some  remarkable  occurrence  in  each  month.  Thus  the  spring  signs 
were  distinguished  for  the  production  of  those  animals  vi^hich  were  held  in  the 
greatest  esteem,  viz.  the  sheep,  the  black-cattle,  and  the  goats ;  the  latter  being 
the  most  prohfic,  were  represented  by  the  figure  of  Gemini. — When  the  sun  enters 
Cancer,  he  discontinues  his  progress  towards  the  north  pole,  and  begins  to  return 
back  towards  the  south  pole.  This  retrograde  motion  was  represented  by  a  Crab, 
which  is  said  to  go  backwards.  The  heat  that  usually  follows  in  the  next  month 
is  represented  by  the  Lion,  an  animal  remarkable  for  its  fierceness,  and  which,  at 
this  season,  was  frequently  impelled,  through  thirst,  to  leave  the  sandy  desert  and 
make  its  appearance  on  the  banks  of  the  Nile.  The  sun  entered  the  6th  sign  about 
the  time  of  harvest,  which  season  was  therefore  represented  by  a  virgin,  or  female 
reaper,  with  an  ear  of  corn  in  her  hand..*  When  the  sun  enters  Libra,  the  days  and 
nights  are  equal  all  over  the  world,  and  seem  to  observe  an  equilibrium,  like  a 
balance. 

Autumn,  which  produces  fruits  in  great  abundance,  brings  with  it  a  variety  of 
diseases ;  this  season  is  represented  by  that  venomous  animal  the  Scorpion,  who 
wounds  with  a  sting  in  his  tail  as  he  recedes.  The  fall  of  the  leaf  was  the  season 
for  hunting,  and  the  stars  which  marked  the  sun's  path  at  this  time  were  repre- 
sented by  a  huntsman,  or  archer,  with  his  arrows  and  weapons  of  destruction. 

The  Goat,  which  delights  in  cUmbing  and  ascending  some  mountain  or  preci- 
pice, is  the  emblem  of  the  winter  solstice,  when  the  sun  begins  to  ascend  from 
the  southern  tropic,  and  gradually  to  increase  in  height  for  the  ensuing  half 
year. 

Aquarius,  or  the  Water-bearer,  is  represented  by  the  figure  of  a  man  pouring 


Chap.  I. 


DEFINITIONS,  &C. 


49 


out  water  from  an  urn,  an  emblem  of  the  dreary  and  uncomfortable  season  of 
winter. 

The  last  of  the  zodiacal  constellations  was  Pisces,  or  a  couple  of  fishes,  lied  back 
to  back,  representing  the  fishing-seasnn.  The  severity  of  the  winter  is  over,  the 
flocks  do  not  afford  sustenance,  but  the  seas  and  rivers  are  open,  and  abound  with 
fish. 

The  Chaldeans  and  Egyptians  were  the  original  inventors  of  astronomy ;  they 
registered  the  events  in  their  history,  and  the  mysteries  of  their  religion  among  the 
stars  by  emblematical  figures.  The  Greeks  displaced  many  of  the  Chaldean  con- 
stellations, and  placed  such  images  as  had  reference  to  their  own  history  in  their 
room.  The  same  method  was  followed  by  the  Romans;  hence  the  accounts  given 
of  the  signs  of  the  zodiac,  and  of  the  constellations,  are  contradictory  and  involved 
in  fable. 

11.  THE  NORTHERN  CONSTELLATIONS. 

Andromeda  is  represented  on  the  celestial  globe  by  the  figure  of  a  woman 
almost  naked,  having  her  arms  extended,  and  chained  by  the  wrist  of  her  right  arm 
to  a  rock.  She  was  the  daughter  of  Cepheus,  king  of  Ethiopia,  who,  in  order  to 
preserve  his  kingdom,  was  obliged  to  tie  her  naked  to  a  rock  near  Joppa,  now  JaflTa. 
in  Syria,  to  be  devoured  by  a  sea-monster;  but  she  was  rescued  by  Perseus,  in  his 
return  from  the  conquest  of  the  Gorgons,  who  turned  the  monster  into  a  rock  by 
showing  it  the  head  of  Medusa.  Andromeda  was  made  a  constellation  after  her 
death,  by  Minerva. 

Antinous  was  a  youth  of  Bithynia,  in  Asia  Minor,  a  great  favourite  of  the  em- 
peror Adrian,  who  erected  a  temple  to  his  memory,  and  placed  him  among  the  con- 
stellations.   Antinous  is  generally  reckoned  a  part  of  the  constellation  Aquila. 

Aquila  is  supposed  to  have  been  Merops,  a  king  of  the  island  of  Cos,  one  of  the 
Cyclades  ;  who,  according  to  Ovid,  was  changed  into  an  eagle,  and  placed  among 
the  constellations. 

AsTERioN  ET  Chara,  vtl  Canes  Venatici,  the  two  greyhounds,  held  in  a  string 
by  Bootes:  they  were  formed  by  Hevelius  out  of  the  Stellce  Informes  of  the  ancient 
catalogues. 

Auriga  is  represented  on  the  celestial  globe  by  the  figure  of  a  man  in  a  kneeling 
or  sitting  posture,  with  a  goat  and  her  kids  in  her  left  hand,  and  a  bridle  in  his  right. 
The  Greeks  give  various  accounts  of  this  constellation ;  some  suppose  it  to  be 
Erichthonius,  the  fourth  king  of  Athens,  and  son  of  Vulcan  and  Minerva;  he  was 
very  deformed,  and  his  legs  resetubled  the  tail  of  serpents  ;  he  is  said  to  have  in- 
vented chariots,  and  the  manner  of  harnessing  horses  to  draw  them.  Others  say 
that  Auriga  is  Mirtilus,  a  son  of  Mercury  and  Phaetusa;  he  was  charioteer  to 
CEnomaus,  k  ing  of  Pisa,  in  Elis,  and  so  experienced  in  riding  and  the  management 
of  horses,  that  he  rendered  those  of  CEnomaus  the  swiftest  in  all  Greece;  his  infi- 
delity to  his  master  proved  at  last  fatal  to  him,  but  being  a  son  of  Mercury,  he  was 
made  a  constellation  after  his  death.  But  as  neither  of  these  fables  seem  to  ac- 
count for  the  goat  and  her  kids,  it  has  been  supposed  that  they  refer  to  Amalthsea, 
daughter  of  Melissus,  king  of  Crete,  who,  in  conjunction  with  her  sister  Melissa, 
fed  Jupiter  with  goat's  milk;  it  is  moreover  said  that  Amalthsea  was  a  goat  called 
Olenia,  from  its  residence  at  Olenus,  a  town  of  Peloponnesus. 

Bootes  is  supposed  to  be  Areas,  a  son  of  Jupiter  and  Calisto;  Juno,  who  was 
jealous  of  Jupiter,  changed  Calisto  into  a  bear;  she  was  near  being  killed  by  her 
son  Areas  in  hunting.  Jupiter,  to  prevent  farther  injury  from  the  huntsmen,  made 
Calisto  a  constellation  of  heaven,  and  on  the  death  of  Areas,  conferred  the  same 
hono'.ir  on  him.  Bootes  is  represented  as  a  man  in  a  walking  posture,  grasping  in 
his  left  hand  a  club,  and  having  his  right  hand  extended  upwards,  holding  the  cord 
of  the  two  dogs  Asterion  and  Chara,  which  seem  to  be  barking  at  the  Great  Bear ; 
hence  Bootes  is  sometimes  called  the  bear-driver,  and  the  office  assigned  him  is  to 
drive  the  two  bears  round  about  the  pole. 


7 


50 


DEFINITIONS,  &C. 


Part  I. 


Camelopardalus  was  formed  by  Hevelius.  The  Caraelopard  is  remarkably  tame 
and  tractable ;  its  natural  properties  resemble  those  of  the  camel,  and  its  body  is 
variegated  with  spots  like  the  leopard.  This  animal  is  found  in  Ethiopia  and  other 
parts  of  Africa;  its  neck  is  about  seven  feet  long,  its  fore  and  hind  legs  from  the 
hoof  to  the  second  joint,  are  nearly  of  the  same  length  ;  but  from  the  second  joint 
of  the  legs  to  the  body,  the  fore  legs  are  so  long  in  comparison  with  the  hind  ones, 
that  the  body  seems  to  slope  like  the  the  roof  of  a  house. 

Cassiopeia  was  the  wife  of  Cepheus,  and  mother  of  Andromeda.  See  these  con- 
stellations, as  also  Cetus. 

Cepheus  was  a  king  of  Ethiopia,  and  the  father  of  Andromeda  by  Cassiopeia ; 
Cepheus  was  one  of  the  Argonauts,  who  went  with  Jason  to  Colchis  to  fetch  the 
golden  fleece. 

Cerberus  was  a  dog  belonging  to  Pluto,  the  god  of  the  infernal  regions;  this 
dog  had  fifty  heads  according  toHesiod,  and  three  according  to  other  mythologists ; 
he  was  stationed  at  the  entrance  of  the  infernal  regions,  as  a  watchful  keeper,  to 
prevent  the  living  from  entering,  and  the  dead  from  escaping  from  their  confine- 
ment. The  last  and  most  dangerous  exploint  of  Hercules,  was  to  drag  Cerberus 
from  the  infernal  regions,  and  bring  him  before  Eurystheus,  king  of  Argos. 

Coma  Berenices  is  composed  of  the  unformed  stars,  between  the  Lion's  Tail  and 
Bootes.  Berenice  was  the  wife  of  Evergetes,  a  surname  signifying  benefactor; 
when  he  went  on  a  dangerous  expedition,  she  vowed  to  dedicate  her  hair  to  the 
goddess  Venus,  if  he  returned  in  safety.  Sometime  after  the  victorious  return  of 
Evergetus,  the  locks  which  were  in  the  temple  of  Venus  disappeared  ;  and  Conon, 
an  astronomer,  publicly  reported  that  Jupiter  had  carried  them  away,  and  made 
them  a  constellation. 

Cor  Caroli,  or  Charles's  heart,  in  the  neck  of  Chara,  the  southernmost  of  the  two 
dogs  held  in  a  string  by  Bootes,  was  so  denominated  by  Sir  Charles  Scarborougb^ 
physician  to  king  Charles  II.  in  honour  of  king  Charles  I. 

Corona  Borealis  is  a  beautiful  crown  given  by  Bacchus,  the  son  of  Jupiter,  to 
Ariadne,  the  daughter  of  Minos,  second  king  of  Crete.  Bacchus  is  said  to  have 
married  Ariadne  after  she  was  basely  deserted  by  Theseus,  king  of  Athens,  and 
after  her  death  the  crown  which  Bacchus  had  given  her  was  made  a  constellation. 

Cygnus  is  fabled  by  the  Greeks  to  be  the  swan  under  the  form  of  which  Jupiter 
deceived  Leda,  or  Nemesis,  the  wife  of  Tyndarus,  king  of  Laconia.  Leda  was  the 
mother  of  Pollux  and  Helena,  the  most  beautiful  woman  of  the  age  ;  and  also  of 
Castor  and  Clytemnestra.  The  two  former  were  deemed  the  offspring  of  Jupiter, 
and  the  others  claimed  Tyndarus  as  their  father. 

Delphinus,  the  dolphin,  was  placed  among  the  constellations  by  Neptune,  be- 
cause, by  means  of  a  dolphin,  Amphitrite  became  the  wife  of  Neptune,  though  she 
had  made  a  vow  of  perpetual  celibacy. 

Draco.  The  Greeks  give  various  accounts  of  this  constellation  ;  by  some  it 
is  represented  as  the  watchful  dragon  which  guarded  the  golden  apples  in  the  gar- 
den of  the  Hesperides,  near  mount  Atlas,  in  Africa;  and  was  slain  by  Hercules: 
Juno,  who  presented  these  apples  to  Jupiter  on  the  day  of  their  nuptials,  took 
Draco  up  to  Heaven,  and  made  a  constellation  of  it  as  a  reward  for  its  faithful  ser- 
vices: others  maintain,  that  in  a  war  with  the  giants,  this  dragon  was  brought  into 
combat,  and  opposed  to  Minerva,  who  seized  it  in  her  hands  and  threw  it,  twisted 
as  it  was,  into  the  heavens  round  the  axis  of  the  earth,  before  it  had  time  to  unwind 
its  contortions. 

EquuLus,  the  little  horse,  or  Equi  Sectio,  the  horse's  head,  is  supposed  to  be  the 
brother  of  Pegasus. 

Hercules  is  represented  on  the  celestial  globe  holding  a  club  in  his  right  hand, 
the  three-headed  dog  Cerberus  in  his  left,  and  the  skin  of  the  Nemaean  Lion  thrown 
over  his  shoulders.  Hercules  was  the  son  of  Jupiter  and  Alcmena,  and  reckoned 
the  most  famous  hero  of  Antiquity. 

Lacerta,  the  Lizard,  was  added  by  Hevelius  to  the  old  constellations. 


Chap.  I. 


DEFINITIONS,  &C. 


51 


Leo  Minor  was  formed  out  of  the  Stell(Z  Informes,  or  unformed  stars  of  the  an- 
cients, and  placed  above  Leo  the  zodiacal  constellation.  According  to  the  Greek 
fables,  Leo  was  the  celebrated  Nemsean  lion  which  had  dropped  from  the  moon, 
but  being  slain  by  Hercules,  was  elevated  to  the  heavens  by  Jupiter,  in  commem- 
oration of  the  dreadful  conflict,  and  in  honour  of  that  hero.  But  this  constellation 
was  amongst  the  Egyptian  hieroglyphics,  long  before  the  invention  of  the  fables 
of  Hercules.  See  the  Zodiacal  Constellations,  p.  48.  Nemsea  was  a  town  of 
ArgoHs  in  Peloponnesus,  and  was  infested  by  a  lion  which  Hercules  slew,  and 
clothed  himself  in  the  skin  j  games  were  instituted  to  commemorate  this  great 
event. 

The  Lynx  was  composed  by  Hevelius  out  of  the  unformed  stars  of  the  ancients, 
between  Auriga  and  Ursa  Major. 

Lyra,  the  lyre  or  harp,  is  included  in  Vultur  Cadens.  This  constellation  was 
at  first  a  tortoise,  afterwards  a  lyre,  because  the  strings  of  the  lyre  were  originally 
fixed  to  the  shell  of  a  tortoise  :  it  is  asserted  that  this  is  the  lyre  which  Apollo  or 
Mercury  gave  to  Orpheus,  and  with  which  he  descended  the  infernal  regions,  in 
search  of  his  wife  Eurydice.  Orpheus  after  death  received  divine  honours,  the 
Muses  gave  an  honourable  burial  to  his  remains,  and  his  lyre  became  one  of  the 
constellations. 

MoNS  MiENALtJs.  The  mountain  Maenalus  in  Arcadia  was  sacred  to  the  god 
Pan,  and  frequented  by  shepherds  ;  it  received  its  name  from  Maenalus,  a  son  of 
Lycaon,  king  of  Arcadia. 

Pegasus,  the  winged  horse,  according  to  the  Greeks,  sprung  from  the  blood  of 
the  Gorgon  Medusa,  after  Perseus,  a  son  of  Jupiter,  had  cut  ofi'her  head.  Pegasus 
fixed  his  residence  on  mount  Hehcon  in  Boeotia,  where,  by  striking  the  earth  with 
his  foot,  he  produced  a  fountain  called  Hippocrene.  He  became  the  favourite  of 
the  Muses,  and  being  afterwards  tamed  by  Neptune,  or  Minerva,  he  was  given  to 
Bellerophon  to  conquer  the  Chimaera,  a  hideous  monster  that  continually  vomited 
flames ;  the  fore-parts  of  its  body  were  those  of  a  lion,  the  middle  was  that  of  a 
goat,  and  the  hinder-parts  were  those  of  a  dragon ;  it  had  three  heads,  viz.  that  of 
a  lion,  a  goat,  and  a  dragon.  After  the  destruction  of  this  monster,  Bellerophon 
attempted  to  fly  to  heaven  upon  Pegasus,  but  Jupiter  sent  an  insect  which  stung 
the  horse,  so  that  he  threw  down  the  rider.  Bellerophon  fell  to  the  earth,  and  Pe- 
gasus continued  his  flight  up  to  heaven,  and  was  placed  by  Jupiter  among  the  con- 
stellations. 

Perseus  is  represented  on  the  globe  with  a  sword  in  his  right  hand,  the  head  of 
Medusa  in  his  left,  and  wings  at  his  ancles.  Perseus  was  the  son  of  Jupiter  and 
Danae.  Pluto,  the  god  of  the  infernal  regions,  lent  him  his  helmet,  which  had  the 
power  of  rendering  its  bearer  invisible ;  Minerva,  the  goddess  of  wisdom,  fur- 
nished him  with  her  buckler,  which  was  as  resplendent  as  glass  ;  and  he  received 
from  Mercury  wings,  and  a  dagger  or  sword ;  thus  equipped,  he  cut  off  the  head 
of  Medusa,  and  from  the  blood  which  dropped  from  it  in  his  passage  through  the 
air,  sprang  an  innumerable  quantity  of  serpents,  which  ever  after  infested  the  sandy 
deserts  of  Lybia.  Medusa  was  one  of  the  three  Gorgons  who  had  the  power  to 
turn  into  stones  all  those  on  whom  they  fixed  their  eyes  ;  Medusa  was  the  only  one 
subject  to  mortality :  she  was  celebrated  for  the  beauty  of  her  locks,  but  having 
violated  the  sanctity  of  the  temple  of  Minerva,  that  goddess  changed  her  locks 
into  serpents.    See  the  constellation  Andromeda, 

Sagitta,  the  arrow.  The  Greeks  say  that  this  constellation  owes  its  origin  to 
one  of  the  arrows  of  Hercules,  with  which  he  killed  the  eagle  or  vulture  that  per- 
petually gnawed  the  liver  of  Prometheus,  who  was  tied  to  a  rock  on  Mount  Cau- 
casus, by  order  of  Jupiter. 

Scutum  Sobieski  was  so  named  by  Hevelius,  in  honour  of  John  Sobieski,  king 
of  Poland.  Hevelius  was  a  celebrated  astronomer,  born  at  Dantzick  :  his  cata- 
logue of  fixed  stars  was  entitled  Firmamentum  Sobieskianum,  and  dedicated  to  the 
king  of  Poland. 

Serpens  is  also  called  Serpens  Ophiuch%  being  grasped  by  the  hands  of  Ophmchus 


52 


DEFINITIONS,  &C. 


Part  L 


Serpentarius,  OphiucuSy  or  Msculapius,  is  represented  with  a  large  beard,  and 
holding  in  his  two  hands  a  serpent.  The  serpent  was  the  symbol  of  medicine, 
and  of  the  gods  who  preside  over  it,  as  Apollo  and  ^sculapius,  because  the  ancient 
physicians  used  serpents  in  their  prescriptions. 

Taurus  Poniatowski  was  called  so  in  honour  of  Count  Poniatowski,  a  Polish 
officer  of  extraordinary  merit,  who  saved  the  life  of  Charles  XII  of  Sweden,  at  the 
battle  of  Pultowa,  a  town  near  the  Dnieper,  about  150  miles  south-east  of  Kiov  ; 
and  a  second  time  at  the  island  of  Rugen,  near  the  mouth  of  the  river  Oder. 

Triangulum.  A  triangle  is  a  well  known  figure  in  geometry  ;  it  was  placed  in 
the  heavens  in  honour  of  the  most  fertile  part  of  Egypt,  being  called  the  delta  of 
the  Nile,  from  its  resemblance  to  the  Greek  letter  of  that  name  The  inven- 

tion of  geometry  is  usually  ascribed  to  the  Egj'ptians,  and  it  is  asserted  that  the 
annual  inundations  of  the  Nile  which  swept  away  the  bounds  and  land-niarks  of 
the  estates,  gave  occasion  to  it,  by  obliging  the  Egyptians  to  consider  the  figure 
and  quantity  belonging  to  the  several  proprietors. 

Ursa  Major  is  said  to  be  Calisto,  an  attendant  of  Diana,  the  goddess  of  hunt- 
ing. Calisto  was  changed  into  a  bear  by  Juno. —  See  the  constellation  Bootes.  It  is 
farther  stated  that  the  ancients  represented  Ursa  Major  and  Ursa  Minor,  each 
under  the  form  of  a  wagon,  drawn  by  a  team  of  horses.  Ursa  Major  is  well 
known  to  the  country  people  at  this  day,  by  the  title  of  Chades\<i  Wain,  or  wagon  : 
in  some  places  it  is  called  the  plough.  There  are  two  remarkable  stars  in  Ursa 
Major,  considered  as  the  hindmost  in  the  square  of  the  wain,  called  the  pointers, 
because  an  imaginary  line  drawn  through  these  stars,  and  extended  upwards,  will 
pass  near  the  pole-star  in  the  tail  of  the  Little  Bear. 

VuLPECULA  ET  Anser,  the  Fox  and  the  Goose,  was  made  by  Hevelius  out  of  the 
unformed  stars  of  the  ancients. 

III.  THE  SOUTHERN  CONSTELLATIONS. 

Ara  is  supposed  to  be  the  altar  on  which  the  gods  swore  before  their  combat 
with  the  giants. 

Argo  Navis  is  said  to  be  the  ship  Argo,  which  carried  Jason  and  the  Argonauts 
to  Colchis  to  fetch  the  golden  fleece. 

Canis  Major,  the  Great  Dog,  according  to  the  Greek  fables,  is  one  of  Orion's 
hounds;  {See  Canis  Minor ;)  but  the  Egyptians,  who  carefully  watched  the  rising 
of  this  constellation,  and  by  it  judged  of  the  swelling  of  the  Nile,  called  the  bright 
star  Siriusthe  centinel  and  watch  of  the  year;  and  according  to  their  hieroglyph- 
ical  mat)ner  of  writing,  represented  it  under  the  figure  of  a  dog.  The  Egyptians 
called  the  Nile  Siris,  and  hence  is  derived  the  name  of  their  deity  Osiris. 

Canis  Minor,  the  Little  Dog,  according  to  the  Greek  fables,  is  one  of  Orion's 
hounds;  but  the  Egyptians  were  most  probably  the  inventors  of  this  constellation, 
and  as  it  rises  before  the  dog-star,  which  at  a  particular  season  was  so  much 
dreaded,  as  it  is  properly  represented  as  a  little  watchful  creature,  giving  notice  of 
the  other's  approach ;  hence  the  Latins  have  called  it  Antecanis,  the  star  before 
the  dog. 

Centaurus.  The  Centauri  were  a  people  of  Thessaly,  half  men  and  half 
horses.  The  Thessalians  were  celebrated  for  their  skill  in  taming  horses,  and  their 
appearance  on  horseback  was  so  uncommon  a  sight  to  the  neighbouring  states, 
that  at  a  distance  they  imagined  the  man  and  horse  to  be  one  animal  :  when  the 
Spaniards  landed  in  America,  and  appeared  on  horseback,  the  Mexicans  had  the 
same  ideas.  This  constellation  is  by  some  supposed  to  represent  Chiron  the  Cen- 
taur, tutor  of  Achilles,  -iEsculapius,  Hercules,  &c. ;  but  as  Sagittarius  is  likewise 
a  Centaur,  others  have  contended  that  Chiron  is  represented  by  Sagittarius. 

Cetus,  the  whale,  is  pretended  by  the  Greeks  to  be  the  sea-monster  which  Nep- 
tune, brother  to  Juno,  sent  to  devour  Andromeda ;  because  her  mother,  CassiO" 
peia,  had  boasted  herself  to  be  fairer  than  Juno  and  the  Nereides. 


Chap.  I. 


DEFINITIONS,  &LC. 


53 


CoRVUs,  the  crow,  was,  according  to  the  Greek  fables,  made  a  constellation  by 
ApoUo:  this  god  being  jealous  of  Coronis,  (the  daughter  of  Phlegyas  and  mother 
of  -^sculapius,)  sent  a  crow  to  watch  her  behaviour;  the  bird,  perched  on  a  tree, 
perceived  her  criminal  partiality  to  Ischys,  the  Thessalian,  and  acquainted  Apollo 
with  her  conduct. 

Crux,  Crusero  or  Crosier.  There  are  four  stars  in  this  constellation  forming 
a  cross,  by  which  mariners  sailing  in  the  southern  hemisphere  readily  find  the 
situation  of  the  Antarctic  pole. 

Eridanus,  the  river  Po,  called  by  Virgil  the  king  of  rivers,  was  placed  in  the 
heavens  for  receiving  Phaeton,  whom  Jupiter  struck  with  thunder-bolts  when  the 
earth  was  threatened  with  a  general  conflagration,  through  the  ignorance  of 
Phoeton,  who  had  presumed  to  be  able  to  guide  the  chariot  of  the  sun.  The  Po  is 
sometimes  called  Orion's  river. 

Htdua  is  the  water  serpent,  which,  according  to  poetic  fable,  infested  the  Lake 
Lerna  in  Peloponnesus :  this  monster  had  a  great  number  of  heads,  and  as  soon  as 
one  was  cut  off,  another  grew  in  its  stead  ;  it  was  killed  by  Hercules.  The  general 
opinion  is,  that  this  Hydra  was  only  a  multitude  of  serpents  which  infested  the 
marshes  of  Lerna. 

Lepus,  the  hare,  according  to  the  Greek  fables,  was  placed  near  Orion,  as  being 
one  of  the  animals  which  he  hunted. 

MiCROscopiUM,  the  microscope,  is  an  optical  instrument  composed  of  lenses  or 
mirrors,  so  arranged  as  to  render  very  minute  objects  clear  and  distinct. 

MoNOCEROS,  the  unicorn,  was  added  by  Hevehus,  and  composed  of  stars  which 
the  ancients  had  not  comprised  within  the  outlines  of  the  other  constellations. 

Orion  is  represented  on  the  globe  by  the  figure  of  a  man  with  a  sword  in  his 
belt,  a  club  in  his  right  hand,  and  the  skin  of  a  lion  in  his  left ;  he  is  said  by  some 
authors  to  be  the  son  of  Neptune  and  Euryale,  a  famous  huntress  ;  he  possessed 
the  disposition  of  his  mother,  became  the  greatest  hunter  in  the  world,  and  boasted 
that  there  was  not  an  animal  on  the  earth  which  he  could  not  conquer.  Others 
say,  that  Jupiter,  Neptune,  and  Mercury,  as  they  travelled  over  Boeolia,  met  with 
great  hospitality  from  Hyrieus,  a  peasant  of  the  country,  who  was  ignorant  of  their 
dignity  and  character.  When  Hyrieus  had  discovered  that  they  were  gods,  he 
welcomed  them  by  the  voluntary  sacrifice  of  an  ox.  Pleased  with  his  piety,  the 
gods  promised  to  grant  him  whatever  he  required,  and  the  old  man,  who  had  lately 
lost  his  wife,  and  to  whom  he  made  a  promise  never  to  marry  again,  desired  them, 
that  as  he  was  childless,  they  would  give  him  a  son  without  obhging  him  to  break 
his  promise.  The  gods  consented,  and  Orion  was  produced  from  the  hide  of  the 
ox. 

Piscis  AusTRALis,  the  southern  fish,  is  supposed  by  the  Greeks  to  be  Venus, 
who  transformed  herself  into  a  fish,  to  escape  from  the  terrible  giant  Typhon. 

RoBUR  Caroli,  or  Charles's  Oak,  was  so  called  by  Dr.  Halley,  in  memory  of  the 
tree  in  which  Charles  IL  saved  himself  from  his  pursuers  after  the  battle  of 
Worcester.  Dr.  Halley  went  to  St.  Helena,  in  the  year  1676,  to  take  a  catalogue 
'    of  such  stars  as  do  not  rise  above  the  horizon  of  London. 

Sextans,  the  sextant,  a  mathematical  instrument  well  known  to  mariners,  was 
formed  by  Hevelius  from  the  Stella  Informes  of  the  ancients. 

92.  Galaxy,  via  lactea,  or  Milky-way^  is  a  whitish  luminous 
'  '  tract  which  seems  to  encompass  the  heavens,  hke  a  girdle,  of  a 
considerable  though  unequal  breadth,  varying  from  about  4  to  20 
degrees.  It  is  composed  of  an  infinite  number  of  small  stars, 
which  by  their  joint  light  occasion  that  confused  whiteness  which 
we  perceive  in  a  clear  night  when  the  moon  does  not  shine  very 
bright.    The  Milky- way  may  be  traced  on  the  celestial  globe, 


54 


DEFINITIONS,,  &C. 


Part  I. 


beginning  at  Cygnus,  through  Cepheus,  Cassiopeia,  Perseus, 
Auriga,  Orion's  club,  the  feet  of  Gemini,  part  of  Monoceros, 
Argo  Navis,  Robur  Caroli,  Crux,  the  feet  of  the  Centaur,  Circinus, 
Quadra  Euclidis,  and  Ara  ;  here  it  is  divided  into  two  parts  ;  the 
eastern  branch  passes  through  the  tail  of  Scorpio,  the  bow  of 
Sagittarius,  Scutum  Sobieski,  the  feet  of  Antinous,  Aquila, 
Sagitta,  and  Vulpecula  ;  the  western  branch  passes  through  the 
upper  part  of  the  tail  of  Scorpio,  the  right  side  of  Serpentarius, 
Taurus  Poniatowski,  the  Goose,  and  the  neck  of  Cygnus,  and 
meets  the  aforesaid  branch  in  the  body  of  Cygnus. 

93.  Nebulous,  or  cloudy,  is  a  term  applied  to  certain  fixed 
stars  smaller  than  those  of  the  sixth  magnitude,  which  only  show 
a  dim  hazy  light  like  little  specks  or  clouds.  In  Prsesepe,  in  the 
breast  of  Cancer,  are  reckoned  36  little  stars  ;  F.  le  Compte 
adds,  that  there  are  40  such  stars  in  the  Pleiades,  and  2500  in 
the  whole  Constellation  of  Orion.  It  may  be  further  remarked, 
that  the  Milky-w^ay  is  a  continued  assemblage  of  Nebulae. 

94.  Bayer's  Characters.  John  Bayer,  of  Augsburg,  in 
Swabia,  published  in  1603,  an  excellent  work,  entitled  Ura7i- 
omttria,  being  a  complete  atlas  of  all  the  constellations,  with  the 
useful  invention  of  denoting  the  stars  in  every  constellation  by 
the  letters  of  the  Greek  and  Roman  Alphabets ;  setting  the  first 
Greek  letter  ci  to  the  principal  star  in  each  constellation,  /3  to  the 
second  in  magnitude,  y  to  the  third,  and  so  on,  and  when  the 
Greek  alphabet  was  finished,  he  began  with  «,  6,  c,  &:c.  of  the 
Roman.  This  useful  method  of  describing  the  stars  has  been 
adopted  by  all  succeeding  astronomers,  who  have  further  enlarged 
it  by  adding  the  numbers  1,  3,  3,  &c.  in  the  same  regular  suc- 
cession, when  any  constellation  contains  more  stars  than  can  be 
marked  by  the  two  alphabets.  The  figures  are,  however,  some- 
times placed  above  the  Greek  letter,  especially  where  double 
stars  occur  ;  for  though  many  stars  may  appear  single  to  the 
naked  eye,  yet  when  viewed  through  a  telescope  of  considerable 
magnifying  power,  they  appear  double,  triple,  &c.  Thus,  in  Dr. 
Zach's  Tabulae  Motuum  Solis,  we  meet  with  /  Tauri,  /3  Tauri, 
7  Tauri,  ^  Tauri,  ^2  Tauri,  &c. 

As  the  Greek  letters  so  frequently  occur  in  catologues  of  the  stars  and  on  the 
celestial  globes,  the  Greek  alphabet  is  here  introduced  for  the  use  of  those  who  are 
unacquainted  with  the  letters.  The  capitals  are  seldom  used  in  the  catalogues  of 
stars,  but  are  here  given  for  the  sake  of  regularity. 


Chap.  L 


DEFINITIONS, 


55 


THE   GREEK  ALPHABET. 


Sound. 

A 

a. 

Alpha 

a 

B  ^ 

Beta 

b 

r 

Gamma 

g 

A 

Delta 

d 

E 

Epsilon 

e  short 

Z 

Zeta 

z 

H 

Eta 

e  long 

0 

Theta 

th 

I 

1 

Iota 

i 

K 

it 

Kappa 

k 

A 

X 

Lambda 

1 

M 

A* 

Mu 

m 

N 

y 

Nu 

n 

S 

Xi 

X 

o 

0 

0  micron 

0  short 

n 

TT  'ST 

.  Pi 

P 

p 

Rho 

r 

CI  • 

feigma 

s 

T 

Tau 

t 

Y 

Upsilori 

u 

Phi 

ph 

X 

Chi 

ch 

Psi 

ps 

i2 

Omega 

o  long 

95.  Planets  are  opaque  bodies,  similar  to  our  earth,  which 
move  round  the  sun  in  certain  periods  of  time.  They  shine  not 
by  their  own  light,  but  by  the  reflection  of  the  light  which  they 
receive  from  the  sun.  The  planets  are  distinguished  into  primary 
and  secondary. 

96.  The  Primary  Planets  regard  the  sun  as  their  centre  of 
motion.  There  are  11  Primary  Planets,  distinguished  by  the  fol- 
lowing characters  and  names,  viz.  ^  Mercury,  2  Venus,  ©  the 
Earth,     Mars,  fi  Vesta,  ?  Juno,  ?  Ceres,  $  Pallas,  U  Jupiter, 

Saturn,  and  ^  the  Georgium  Sidus. 

97.  The  Secondary  Planets,  satellites,  or  moons,  regard  the 
primary  planets  as  their  centres  of  motion  :  thus  the  moon  re- 
volves round  the  earth,  the  satellites  of  Jupiter  move  round  Jupi- 
ter, &:c.  There  are  18  secondary  planets.  The  earth  has  one 
satellite,  Jupiter  four,  Saturn  seven,  and  the  Georgium  Sidus  six, 

98.  The  Orbit  of  a  planet  is  the  imaginary  path  it  describes 
round  the  sun.    The  earth's  orbit  is  in  the  plane  of  the  ecliptic. 


56 


DEFINITIONS,  &C. 


Part  L 


99.  Nodes  are  the  two  opposite  points  where  the  orbit  of  a 
planet  seems  to  intersect  the  ecliptic.  That  where  the  planet  ap- 
pears to  ascend  from  the  south  to  the  north  side  of  the  ecliptic,  is 
called  the  ascending  or  north  node,  and  is  marked  thus  Q> ;  and 
the  opposite  point  where  the  planet  appears  to  descend  from  the 
north  to  the  south,  is  called  the  descending  or  south  node,  and  is 
marked 

100.  Aspect  of  the  stars  or  planets  is  their  situation  with  res- 
pect to  each  other.  There  are  five  aspects,  viz.  6  Conjunction^ 
when  they  are  in  the  same  sign  and  degree  ;  Sextile,  when  they 
are  two  signs,  or  a  sixth  part  of  a  circle,  distant ;  □  Quartile,  when 
they  are  three  signs,  or  a  fourth  part  of  a  circle,  from  each  other ; 
^  Trine,  when  they  are  four  signs,  or  a  third  part  of  a  circle,  from 
each  other ;  §  Opposition,  when  they  are  six  signs,  or  half  a  cir- 
cle, from  each  other. 

The  conjunction  and  opposition  (particularly  of  the  moon)  are 
called  the  Syzygies ;  and  the  quartile  aspect,  the  Quadratures, 

101.  Direct.  A  planet's  motion  is  said  to  be  direct,  when  it 
appears  (to  a  spectator  on  the  earth)  to  go  forward  in  the  zodiac, 
according  to  the  order  of  the  signs. 

102.  Stationary.  A  planet  is  said  to  be  stationary,  when  (to 
an  observer  on  the  earth),  it  appears  for  some  time  in  the  same 
point  of  the  heavens. 

103.  Retrograde.  A  planet  is  said  to  retrograde,  when  it 
apparently  goes  backward,  or  contrary  to  the  order  of  the  signs, 

104.  Digit,  the  twelfth  part  of  the  sun  or  moon's  apparent  di- 
ameter. 

105.  Disc,  the  face  of  the  sun  or  moon,  such  as  they  appear  to 
a  spectator  on  the  earth ;  for  though  the  sun  and  moon  be  really 
spherical  bodies,  they  appear  to  be  circular  planes. 

106.  Geocentric  latitudes  and  longitudes  of  the  planets  are 
their  latitudes  and  longitudes,  as  seen  from  the  earth. 

107.  Heliocentric  latitudes  and  longitudes  of  the  planets  are 
their  latitudes  and  longitudes,  as  they  would  appear  to  a  spectator 
situated  in  the  sun. 

108.  Apogee,  or  Apogseum,  is  that  point  in  the  orbit  of  a 
planet,  the  moon,  &c.  which  is  farthest  from  the  earth. 

109.  Perigee,  or  Perigseum,  is  that  point  in  the  orbit  of  a 
planet,  the  moon,  &c.  which  is  nearest  to  the  earth. 

110.  Aphelion,  or  Aphelium,  is  that  point  in  the  orbit  of  the 
earth,  or  of  any  other  planet,  which  is  farthest  from  the  sun.  This 
point  is  called  the  higher  Apsis. 


Chap,  L 


DEFINITIONS,  &C. 


57 


111.  Perihelion,  or  Periheliam,  is  that  point  in  the  orbit  of  the 
earth,  or  of  any  other  planet,  which  is  nearest  to  the  sun.  This 
point  is  called  the  lower  Apsis. 

112.  Line  of  the  Apsides  is  a  straight  line  joining  the  higher 
and  lower  apsis  of  a  planet ;  viz.  a  line  joining  the  Aphelium  and 
Perihelium. 

113.  Eccentricity  of  the  orbit  of  any  planet  is  the  distance 
between  the  sun  and  the  centre  of  the  planet's  orbit. 

114.  OccuLTATiON  is  the  obscuration  or  hiding  from  our  sight 
any  star  or  planet,  by  the  interposition  of  the  body  of  the  moon, 
or  of  some  other  planet. 

115.  Transit  is  the  apparent  passage  of  any  planet  over  the 
face  of  the  sun,  or  over  the  face  of  another  planet.  Mercury  and 
Venus,  in  their  transits  over  the  sun's  disc,  appear  like  dark 
specks. 

116.  Eclipse  of  the  Sun  is  an  occultation  of  part  of  the  face 
of  the  sun,  occasioned  by  an  interposition  of  the  moon  between 
the  earth  and  the  sun  ;  consequently  all  eclipses  of  the  sun  hap- 
pen at  the  time  of  new  moon. 

117.  Eclipse  of  the  Moon  is  a  privation  of  the  light  of  the 
inoon,  occasioned  by  an  interposition  of  the  earth  between  the 
sun  and  the  moon ;  consequently  all  eclipses  of  the  moon  happen 
at  full  moon. 

118.  Elongation  of  a  planet  is  the  angle  formed  by  tv^o  lines 
drawn  from  the  earth,  the  one  to  the  sun,  and  the  other  to  the 
planet.* 

119.  Diurnal  Arc  is  the  arc  described  by  the  sun,  moon,  or 
stars,  from  their  rising  to  their  setting. — The  sun's  semi-diurnal 
arc  is  the  arc  described  in  half  the  length  of  the  day. 

120.  Nocturnal  Arc  is  the  arc  described  by  the  sun,  moon, 
or  stars,  from  their  setting  to  their  rising. 

121.  Aberration  is  an  apparent  motion  of  the  celestial  bodies, 
occasioned  by  the  earth's  annual  motion  in  its  orbit,  combined  with 
the  progressive  motion  of  light. 

To  illustrate  this  definition,— If  light  be  supposed  to  have  a  progressive  motion, 
the  position  of  a  telescope  through  which  a  star  is  viewed  must  be  different  from 
that  which  it  would  have  been,  if  light  had  been  instantaneous,  and  therefore  the 


*  This  and  some  of  the  preceding  definitions  are  given  to  illustrate  the  38th  and 
39th  pages  of  White's  Ephemeris,  called  Speculum  Phcenomenorum.  The  words 
elong.  max.  signify  the  greatest  elongation  of  a  planet.  In  Plate  II.  Fig.  2.  E  rep- 
resents the  Earth,  V  Venus,  and  S  the  Sun.  The  elongation  is  the  angle  VES, 
measured  by  the  arc  VS. 

8 


58 


DEFINITIONS,  &C. 


Part  I. 


situation  of  a  star  measured  in  the  heavens,  will  be  different  from  its  true  situation. 
Let  ^  represent  the  situation  of  a  fixed  star,  a  b  the  direction  of  the  earth's  mo- 
tion, ^  B  the  direction  of  a  particle  of  hght,  entering  the  axis  mo  of  a  telescope  at  o, 
and  moving  through  o  b  whilst  the  earth  moves  from  m  to  b,  then  if  the  telescope  be 
kept  parallel  to  itself,  the  light  will  descend  in  the  axis. 

For,  let  the  axis  nd,  se  continue  parallel  to  mo,  then 
if  each  motion  be  considered  as  uniform,  (that  of  the 
spectator  occasioned  by  the  earth's  rotation,  being  dis- 
regarded, because  it  is  so  small  as  to  produce  no  effect,) 
the  spaces  described  in  the  same  time  will  retain  the 
same  ratio  ;  now  ?nB  and  ob  being  described  in  the 
same  time,  and  because  ?nB  :  ob  :  :  mn :  op,  it  follows 
that  mn  and  op  are  also  described  in  the  same  portion 
of  time,  and  therefore  when  the  telescope  is  in  the  sit- 
uation nd  the  particle  of  light  will  be  at  p  in  the  tele- 
scope, and  this  being  the  case  in  every  moment  of  its 
descent,  the  situation  of  the  star,  measured  by  the  tel- 
escope at  B  is  s,  and  the  angle  ^  bs  is  the  aberration. 
Hence  it  appears,  that  if  we  take  bs  :  br  :  :  the  velo- 
city of  hght :  the  velocity  of  the  earth,  and  complete 
the  parallelogram  brss,  the  aberration  will  be  equal  to 
the  angle  bsr  or  sb5  ;  s  will  be  the  true  place  of  the 
star,  and  s  the  place  measured  by  the  instrument,  or 
its  situation  as  seen  by  the  naked  eye. 


122.  Centripetal  Force  is  that  force  with  which  a  moving 
body  is  perpetually  urged  towards  the  centre,  and  made  to  re- 
volve in  a  curve  instead  of  proceeding  in  a  straight  line,  for  all 
motion  is  naturally  rectilinear. — Centripetal  force,  attraction,  and 
gravitation,  are  terms  of  the  same  import. 

123.  Centrifugal  force  is  that  force  with  which  a  body  revolv- 
ing about  a  centre,  or  about  another  body,  endeavours  to  recede 
from  the  curve  which  it  describes.  This  force  is  the  consequence 
of  that  law  of  motion,  by  which  a  body  uninfluenced  by  any  ex- 
ternal force,  necessarily  describes  a  straight  line.  When  a  body 
is  compelled  to  describe  a  curve  line,  it  is,  according  to  this  law, 
disposed  at  every  instant  of  the  description  to  leave  the  curve,  and 
proceed  in  the  direction  of  the  tangent.  When  a  body  describes 
the  circumference  of  a  circle,  by  virtue  of  a  centripetal  force  di- 
rected towards  the  centre  of  the  circle,  the  centrifugal  force  of 
the  body  is  directly  opposed  to  the  centripetal  force,  and  is  equal 
to  it  in  quantity.  By  the  diurnal  motion  of  the  earth  on  its  axis, 
every  particle  of  the  earth  not  situated  in  the  axis  describes  a  cir- 
cle, and  by  its  natural  disposition  to  move  in  a  straight  line,  would 
recede  from  a  circle  in  the  direction  of  the  tangent,  unless  it  were 
retained  by  the  force  of  gravity.  In  this  case,  the  velocities  of  the 
particles  are  proportional  to  their  distances  from  the  axis,  and  the 
centrifugal  forces  of  the  particles  are  also  proportional  to  the  same 
distances. 


Chap.  I. 


GEOGRAPHICAL  THEOREMS. 


59 


Sir  Isaac  Newton  has  demonstrated,  (Princip.  Prop.  XIX.  Book  III.)  that  "  the 
"  centrifugal  force  of  bodies  at  the  equator,  is  to  the  centrifugal  force  with  which 
"bodies  recede  from  the  earth,  in  the  latitude  of  Paris,  in  the  duplicate  ratio  of  the 
"radius  to  the  co-sine  of  the  latitude. — And,  that  the  centripetal  power  in  the  lati- 
"tude  of  Paris,  is  to  the  centrifugal  force  at  the  equator  as  289  is  to  1." 

GEOGRAPHICAL  THEOREMS. 

1.  The  latitude  of  any  place  is  equal  to  the  elevation  of  the  po- 
lar star  (nearly)  above  the  horizon  ;  and  the  elevation  of  the  equa- 
tor above  the  horizon,  is  equal  to  the  complement  of  the  latitude, 
or  what  the  latitude  wants  of  90  degrees. 

2.  All  places  lying  under  the  equinoctial,  or  on  the  equator, 
have  no  latitude,  and  all  places  situated  on  the  first  meridian  have 
no  longitude  ;  consequently  that  particular  point  on  the  globe 
where  the  first  meridian  intersects  the  equator,  has  neither  latitude 
nor  longitude. 

3.  The  latitudes  of  places  increase  as  their  distances  from  the 
equator  increase.  The  greatest  latitude  a  place  can  have  is  90 
degrees. 

4.  The  longitudes  of  places  increase  as  their  distances  from  the 
first  meridian  increase,  reckoned  on  the  equator.  The  greatest 
longitude  a  place  can  have  is  180  degrees,  being  half  the  circum- 
ference of  the  globe  at  that  place ;  hence  no  two  places  can  be 
at  a  greater  distance  from  each  other  than  180  degrees. 

5.  The  sensible  horizon  varies  as  we  travel  from  one  place  to 
another,  and  its  semi-diameter  is  aflfected  by  refraction. 

6.  All  countries  upon  the  face  of  the  earth,  in  respect  to  time, 
equally  enjoy  the  light  of  the  sun,  and  are  equally  deprived  of  the 
benefit  of  it ;  that  is,  every  inhabitant  of  the  earth  has  the  sun 
above  his  horizon  for  six  months,  and  below  his  horizon  for  the 
same  length  of  time.* 


*  This,  though  nearly  true,  is  not  accurately  so.  The  refraction  in  high  latitudes 
is  very  considerable,  (see  definition  85th,)  and  near  the  poles  the  sun  will  be  seen 
for  several  days  before  he  comes  above  the  horizon ;  and  he  will,  for  the  same  reas- 
on, be  seen  for  several  days  after  he  has  descended  below  the  horizon. — The  inhab- 
itants of  the  poles  (if  any)  enjoy  a  very  large  degree  of  twilight,  the  sun  being  near- 
ly two  months  before  he  retreats  18  degrees  below  the  horizon,  or  to  the  point 
where  his  rays  are  first  admitted  into  the  atmosphere,  and  he  is  only  two  months 
more  before  he  arrives  at  the  same  parallel  of  latitude  ;  and  particularly  near  the 
north-pole,  the  light  of  the  moon  is  greatly  increased  by  the  reflection  of  the  snow, 
and  the  brightness  of  the  Aurora  Borealis ;  the  sun  is  likewise  about  seven  days 
longer  in  passing  through  the  northern,  than  through  the  southern  signs  ;  that  is, 
from  the  vernal  equinox,  which  happens  on  the  21st  of  March,  to  the  autumnal  equi- 
nox, which  falls  on  the  23d  of  September,  being  the  summer  half-year  to  the  inhab- 
itants of  north  latitude,  is  186  days,  the  winter  half-year  is  therefore  only  179  days. 
The  inhabitants  near  the  north-pole  have  consequently  more  light  in  the  course  of 
a  year,  than  any  other  inhabitants  on  the  surface  of  the  globe. 


60 


GEOGRAPHICAL  THEOREMS. 


Part  1. 


7.  In  all  places  of  the  earth,  except  exactly  under  the  poles,  the 
days  and  nights  are  of  an  equal  length,  (viz.  12  hours  each,)  when 
the  sun  has  no  declination,  that  is,  on  the  21st  of  March,  and  on 
the  23d  of  September. 

8.  In  all  places  situated  on  the  equator,  the  days  and  nights  are 
always  equal,  notwithstanding  the  alteration  of  the  sun's  declina- 
tion from  north  to  south,  or  from  south  to  north. 

9.  In  all  places,  except  those  upon  the  equator,  or  at  the  two 
poles,  the  days  and  nights  are  never  equal,  but  when  the  sun  en- 
ters the  signs  of  Aries  and  Libra,  viz.  on  the  21st  of  March,  and 
on  the  23d  of  September. 

10.  In  all  places  lying  under  the  same  parallel  of  latitude,  the 
days  and  nights,  at  any  particular  time,  are  always  equal  to  each 
other. 

11.  The  increase  of  the  longest  days  from  the  equator  north- 
ward or  southward,  does  not  bear  any  certain  ratio  to  the  increase 
of  latitude  ;  if  the  longest  days  increase  equally,  the  latitude  in- 
crease unequally.    This  is  evident  from  the  table  of  climates. 

12.  To  all  places  in  the  torrid  zone,  the  morning  and  evening 
twilight  are  the  shortest ;  to  all  places  in  the  frigid  zones  the 
longest ;  and  to  all  places  in  the  temperate  zones,  a  medium  be- 
tween the  other  two. 

13.  To  all  places  lying  within  the  torrid  zone,  the  sun  is  vertical 
twice  a  year ;  to  those  under  each  tropic,  once  ;  but  to  those  in 
the  temperate  and  frigid  zones,  it  is  never  vertical. 

14.  At  all  places  in  the  frigid  zones,  the  sun  appears  every  year 
without  setting  for  a  certain  number  of  days,  and  disappears  for 
nearly  the  same  length  of  time ;  and  the  nearer  the  place  is  to 
the  pole,  the  longer  the  sun  continues  without  setting ;  viz.  the 
length  of  the  longest  days  and  nights  increase  the  nearer  the  place 
is  to  the  pole. 

15.  Between  the  end  of  the  longest  day,  and  the  beginning  of 
the  longest  night,  in  the  frigid  zone,  and  between  the  end  of  the 
longest  night,  and  the  beginning  of  the  longest  day,  the  sun  rises 
and  sets  as  at  other  places  on  the  earth. 

16.  At  all  places  situated  under  the  arctic  or  antarctic  circles, 
the  sun  when  he  has  23°  28'  declination,  appears  for  24  hours  with- 
out setting  ;  but  rises  and  sets  at  all  other  times  of  the  year. 

17.  At  all  places  between  the  equator  and  the  north  pole,  the 
longest  day  and  the  shortest  "night  are  when  the  sun  has  (23°  28') 
the  greatest  north  declination  ;  and  the  shortest  day  and  longest 
night  are  when  the  sun  has  the  greatest  south  declination. 

18.  At  all  places  between  the  equator  and  the  south-pole,  the 
longest  day  and  the  shortest  night  are  when  the  sun  has  (23°  28') 


Chap.  I. 


GEOGRAPHICAL  THEOREMS. 


61 


the  greatest  south  decHnation  ;  and  the  shortest  day  and  longest 
night  are  when  the  sun  has  the  greatest  north  decHnation. 

19.  At  all  places  situated  on  the  equator,  the  shadow  at  noon 
of  an  object,  placed  perpendicular  to  the  horizon,  falls  towards  the 
north  for  one  half  of  the  year,  and  towards  the  south  the  other  half. 

20.  The  nearer  any  place  is  to  the  torrid  zone,  the  shorter  the 
meridian  shadow  of  an  object  will  be.  When  the  sun's  altitude  is 
45  degrees,  the  shadow  of  any  perpendicular  object  is  equal  to 
its  height. 

21.  The  farther  any  place  (situated  in  the  temperate  or  torrid 
zones)  is  from  the  equator,  the  greater  the  rising  and  setting  am- 
plitude of  the  sun  will  be. 

22.  All  places  situated  under  the  same  meridian,  so  far  as  the 
globe  is  enlightened,  have  noon  at  the  same  time. 

23.  If  a  ship  set  out  from  any  port,  and  sail  round  the  earth 
eastward  to  the  same  port  again,  the  people  in  that  ship,  in  reck- 
oning their  time,  will  gain  one  complete  day  at  their  return,  or 
count  one  day  more  than  those  who  reside  at  the  same  port.  If 
they  sail  westward  they  will  lose  one  day,  or  reckon  one  day  less. 
To  illustrate  this,  suppose  the  person  w^ho  travels  westward  should 
keep  pace  with  the  sun,  it  is  evident  he  would  have  continual  day, 
or  it  would  be  the  same  day  to  him  during  his  tour  round  the  earth  ; 
but  the  people  who  remained  at  the  place  he  departed  from  have 
had  night  in  the  same  time,  consequently  they  reckon  a  day  more 
than  he  does. 

24.  Hence,  if  two  ships  should  set  out  at  the  same  time,  from 
any  port,  and  sail  round  the  globe,  the  one  eastward  and  the  other 
westward,  so  as  to  meet  at  the  same  port  on  any  day  whatever, 
they  will  differ  two  days  in  reckoning  their  time  at  their  return. 
If  they  sail  twice  round  the  earth,  they  will  ditfer  four  days  ;  if 
thrice,  six,  &c. 

25.  But,  if  two  ships  should  set  out  at  the  same  time  from  any 
port  and  sail  round  the  globe,  northward  or  southward,  so  as  to 
meet  at  the  same  port  on  any  day  whatever,  they  will  not  differ  a 
minute  in  reckoning  their  time,  nor  from  those  who  reside  at  the 
port. 


GENERAL    PROPERTIES  OP  MATTER. 


Part  I. 


Chapter  II. 

Of  the  General  Properties  of  Matter  and  the  Laws  of  Motion, 

1.  Matter  is  a  substance  which,  by  its  different  modifications, 
becomes  the  object  of  our  five  senses  ;  viz.  v^hatever  vs^e  can  see, 
hear,  feel,  taste,  or  smell,  must  be  considered  as  matter,  being  the 
constituent  parts  of  the  universe. 

2.  The  properties  of  matter  are  extension,  figure,  solidity, 
motion,  divisibility,  gravity,  and  vis  inertiae.  These  properties, 
vi^hich  Sir  Isaac  Newton  observes*  are  the  foundation  of  all  phi- 
losophy, extend  to  the  minutest  particles  of  matter. 

3.  Extension,  when  considered  as  a  property  of  matter,  has 
length,  breadth,  and  thickness. 

4.  Figure  is  the  boundary  of  extension  ;  for  every  finite  exten- 
sion is  terminated  by,  or  comprehended  under,  some  figure. 

5.  Solidity  is  that  property  of  matter  by  which  it  fills  space  ; 
or,  by  w^hich  any  portion  of  matter  excludes  every  other  portion 
from  that  space  which  it  occupies.  This  is  sometimes  defined  the 
impenetrability  of  matter. 

6.  Motion.  Though  matter  of  itself  has  no  ability  to  move, 
yet  as  all  bodies,  upon  which  we  can  make  suitable  experiments, 
have  a  capacity  of  being  transferred  from  one  place  to  another, 
we  infer  that  motion  is  a  quality  belonging  to  all  matter. 

7.  Divisibility  of  matter  signifies  a  capacity  of  being  separated 
into  parts,  either  actually  or  mentally.  That  matter  is  thus  divisi- 
ble, we  are  convinced  by  daily  experience,  but  how  far  the  divis- 
ion can  be  actually  carried  on  is  not  easily  seen.  The  parts  of  a 
body  may  be  so  far  divided  as  not  to  be  sensible  to  the  sight ;  and  by 
the  help  of  microscopes  we  discover  myriads  of  organized  bodies 
totally  unknown  before  such  instruments  were  invented.  A  grain 
of  leaf  gold  will  cover  fifty  square  inches  of  surfacef,  and  contains 
two  millions  of  visible  parts  ;  but  the  gold  which  covers  the  silver 
wire,  used  in  making  gold  lace,  is  spread  over  a  surface  twelve 
times  as  great.  From  such  considerations  as  these,  we  are  led  to 
conclude,  that  the  division  of  matter  is  carried  on  to  a  degree  of 
minuteness  far  exceeding  the  bounds  of  our  faculties. 

Mathematicians  have  shown  that  a  Une  may  be  indefinitely  divided,  as  follows, 


*  Newton's  Princip.  Book  III. — The  third  rule  of  reasoning  in  philosophy, 
t  Adams'  Natural  and  Experimental  Philosophy.   Lect.  XXIV. 


Chap.  II. 


GENERAL  PROPERTIES  OF  MATTER. 


63 


Draw  any  line  ac,  and  another  bm  perpendicular  to  it,  of  ^ 
an  unlimited  length  towards  q;  and  from  any  point  d,  in  ac, 
draw  DE,  parallel  to  bm.  Take  any  number  of  points,  p,  o, 
N,  M,  in  BQ  ;  then  from  p  as  a  centre,  and  the  distance  pb, 
describe  the  arc  bjo,  and  in  the  same  manner  with  o,  n,  m,  as 
centres,  the  distances  ob,  nb,  and  mb  describe  the  arcs  bo, 
Bn,  Bm.  Now  it  is  evident  the  farther  the  centre  is  taken 
from  B,  the  nearer  the  arcs  will  approach  to  d,  and  the  Hne 
ED  will  be  divided  into  parts,  each  smaller  than  the  preceding 
one  ,  and  since  the  line  bm  may  be  extended  to  an  indefin- 
ite distance  beyond  q,  the  Hne  ed,  maybe  indefinitely  dimin- 
ished, yet  it  can  never  be  reduced  to  nothing,  because  an 
arc  of  a  circle  can  never  coincide  with  a  straight  line  bc,  hence  it  follows  that  ed 
may  be  diminished  ad  infiniium. 


8.  Gravity  is  that  force  by  which  a  body  endeavours  to  de- 
scend towards  the  centre  of  the  earth.  By  this  power  of  attrac- 
tion in  the  earth,  all  bodies  on  every  part  of  its  surface  are  pre- 
vented from  leaving  it  altogether,  and  people  move  round  it  in  all 
directions,  without  any  danger  of  falling  from  it. — By  the  influence 
of  attraction,  bodies,  or  the  constituent  parts  of  bodies,  accede  or 
have  a  tendency  to  accede  to  each  other,  without  any  sensible 
material  impulse,  and  this  principle  is  universally  disseminated 
through  the  universe,  extending  to  every  particle  of  matter. 

9.  Vis  Inertije  is  that  innate  force  of  matter  by  which  it  re- 
sists any  change.  We  cannot  move  the  least  particle  of  matter 
without  some  exertion,  and  if  one  portion  of  matter  be  added  to 
another,  the  inertia  of  the  whole  is  increased  ;  also  if  any  part  be 
removed,  the  inertia  is  diminished.  Hence,  the  vis  inertias  of  any 
body  is  proportional  to  its  weight. 

10.  Absolute  and  relative  motion.  A  body  is  said  to  be 
in  absolute  motion,  when  its  situation  is  changed  with  respect  to 
some  other  body  or  bodies  at  rest ;  and  to  be  relatively  in  mo- 
tion, when  compared  with  other  bodies  which  are  likewise  in  mo- 
tion. 

When  a  body  always  passes  over  equal  parts  of  space  in  equal 
successive  portions  of  time,  its  motion  is  said  to  be  uniform. 

When  the  successive  portions  of  space,  described  in  equal 
times,  continually  increase,  the  motion  is  said  to  be  accelerated  ; 
and  if  the  successive  portions  of  space  continually  decrease,  the* 
motion  is  said  to  be  retarded.  Also,  the  motion  is  said  to  be  uni- 
formly accelerated  or  retarded,  when  the  increments  or  decre- 
ments of  the  spaces,  described  in  equal  successive  portions  of 
time,  are  always  equal. 


64 


OF  THE  LAWS  OF  MOTION. 


Part  L 


11.  The  VELOCITY  of  a  body,  or  the  rate  of  its  motion,  is  meas- 
ured by  the  space  uniformly  described  in  a  given  time. 

12.  Force.  Whatever  changes,  or  tends  to  change,  the  state 
of  rest  or  motion  of  a  body,  is  called /brce.  If  a  force  act  but  for 
a  moment,  it  is  called  the  force  of  percussion  or  impulse  ;  if  it  act 
constantly,  it  is  called  an  accelerative  force ;  if  constantly  and 
equally,  it  is  called  an  uniform  accelerative  force. 

general  laws  of  motion. 

Law  I.  "  Every  body  perseveres  in  its  state  of  rest,  or  uniform  mo- 
^Hion  in  a  straight  line,  unless  it  is  compelled  to  change  that  state 
"  by  forces  impressed  thereon." — Newton's  Princip.  Book  1.*= 

Thus  when  a  body  a  is  positively  at  rest,  if^Q  • 

no  external  force  put  it  in  motion,  it  will  always  B 
continue  at  rest.  But  if  any  impulse  be  given 
to  it  in  the  direction  a  b,  unless  some  obstacle,  or  new  force,  stop 
or  retard  its  motion,  it  will  continue  to  move  on  uniformly,  for 
ever,  in  the  same  direction  ab. — Hence  any  projectile,  as  a  ball 
shot  from  a  cannon,  an  arrow  from  a  bow,  a  stone  cast  from  a 
sling,  &:c.  would  not  deviate  from  its  first  direction,  or  tend  to  the 
earth,  but  would  continue  in  a  straight  line  with  an  uniform  mo- 
tion, if  the  action  of  gravity  and  the  resistance  of  the  air  did  not 
alter  and  retard  its  motion. 

Law  II.  "  The  alteration  of  motion,  or  the  motion  generated  or  de- 
"  stroyed,  in  any  body,  is  proportioned  to  the  force  applied ;  and 
"  is  made  in  the  direction  of  that  straight  line  in  which  the  force 
"  acts," — Newton's  Princip.  Book  I. 

Thus,  if  any  motion  be  generated  by  a  given  force,  a  double 
motion  will  be  produced  by  a  double  force,  a  triple  motion  by  a 
triple  force,  &;c. — -and  considering  motion  as  an  effect,  it  will  al- 
ways be  found  that  a  body  receives  its  motion  in  the  same  direc- 
tion with  the  cause  that  acts  upon  it. — If  the  causes  of  motion  be 
various,  and  in  different  directions ;  the  body  acted  upon  must 
take  an  oblique  or  compound  direction*  Hence  a  curvilinear 
motion  must  arise  from  the  continued  action  of  a  force  which  has 


*  This  and  the  two  following  are  generally  termed  J^ewton's  three  laws  of  mo- 
tion ;  but  that  he  was  not  the  first  inventor  of  them  is  evident,  since  they  are  in 
Des  Cartes's  Principia  Philosophic,  Part  II.  pages  38,  39,  and  40,  which  work  was 
published  before  J^ewtovi's  Principia. 


Chap.  II. 


OF  THE  LAWS  OF  MOTION. 


65 


not  a  direction  coincident  with  or  opposite  to  that  of  the  mov- 
ing body. 

Law  III.  "  To  every  action  there  is  always  opposed  an  equal  re- 
action ;  or,  the  mutual  actions  of  two  bodies  upon  each  other  are 
always  equal,  and  directed  to  contrary  points — Newton^s 
Princip.  Book  I. 

If  v/e  endeavour  to  raise  a  weight  by  means  of  a  lever,  we 
shall  find  the  lever  press  the  hands  with  the  same  force  which 
we  exert  upon  it  to  raise  the  weight.  Or  if  we  press  one  scale 
of  a  balance,  in  order  to  raise  a  weight  in  the  other  scale,  the 
pressure  against  the  finger  will  be  equal  to  that  force  with  which 
the  other  scale  endeavours  to  descend. 

When  a  cannon  is  fired,  the  impelling  force  of  the  powder  acts 
equally  on  the  breech  of  the  cannon  and  on  the  ball,  so  that  if 
the  cannon,  with  its  carriage,  and  the  ball  were  of  equal  weight, 
the  carriage  would  recoil  with  the  same  velocity  as  that  with 
which  the  ball  issues  out  of  the  cannon.  But  the  heavier  any 
body  is,  the  less  will  its  velocity  be,  provided  the  force  which 
communicates  the  motion  continues  the  same.  Therefore,  so 
many  times  as  the  cannon  and  carriage  are  heavier  than  the  ball, 
just  so  many  times  will  the  velocity  of  the  cannon  be  less  than 
that  of  the  ball. 

COMPOUND  MOTION. 

1.  If  two  forces  act  at  the  same  time  on  any  body,  and  in  the 
same  direction,  the  body  will  move  quicker  than  it  would  by  being 
acted  upon  by  only  one  of  the  forces, 

%  If  a  body  be  acted  upon  by  two  equal  forces,  in  exactly  oppo- 
site directions,  it  will  not  be  moved  from  its  situation. 

3.  If  a  body  be  acted  upon  by  two  unequal  forces,  in  exactly  con- 
trary  directions,  it  will  move  in  the  direction  of  the  greater  force. 

4t.  If  a  body  be  acted  upon  by  two  forces,  neither  in  the  same  nor 
opposite  directions,  it  will  not  follow  either  of  the  forces,  but  move  r 
in  a  line  between  them. 

The  first  three  of  the  preceding  articles  may  be  considered  as    ^  - 
axioms,  being  self-evident ;  the  fourth  may  be  thus  elucidated : 
Let  a  force  be  applied  to  a  body  at  a,  in  ^      E    K  B 
the  direction  ab,  which  would  cause  it  to 
move  uniformly  from  a  to  b  in  a  given  pe-  PI  - 
riod  of  time  ;  and,  at  the  same  instant,  let 
another  force  be  applied  in  the  direction  C 
AC,  such  as  would  cause  the  body  to  move  from  a  to  c  in  the 

9 


66 


OF  THE  LAWS  OF  MOTION. 


Part  I. 


same  time,  which  the  first  force  would  cause  it  to  move  from  a 
to  B ;  by  the  joint  action  of  these  forces,  the  body  will  describe 
the  diagonal  ad  of  a  parallelogram*  with  an  uniform  motion,  in 
the  same  time  in  which  it  would  describe  one  of  the  sides  ab  or 
AC  by  one  of  the  forces  alone. 

For,  suppose  a  tube  equal  in  length  to  ab  (in  which  a  small 
ball  can  move  freely  from  a  to  b)  to  be  moved  parrallel  to  itself 
from  A  to  G,  describing  with  its  two  extremities  the  lines  ac  and 
BD,  so  that  the  ball  may  move  in  the  tube  from  a  to  b  in  the  same 
time  that  the  tube  has  descended  to  cd  ;  it  is  evident,  that  when 
the  tube  ab  coincides  with  the  line  cd,  the  ball  will  be  at  the  ex- 
tremity D  of  the  line,  and  that  it  has  arrived  there  in  the  same 
time  it  would  have  described  either  of  the  sides  ab  or  ac.  The 
ball  will  likewise  describe  the  straight  line  ad,  for  by  assuming 
several  similar  parallelograms  aegf,  akih,  &c.  it  will  appear,  that 
while  the  ball  has  moved  from  a  to  e  the  tube  will  have  descended 
from  A  to  F,  consequently  the  ball  will  be  at  g  ;  and  while  the 
ball  has  moved  from  a  to  k,  the  tube  will  have  descended  from 
A  to  H,  and  the  ball  will  be  at  i.  Now  agid  is  a  straight  line ; 
for  smaller  parallelograms  that  are  similar  to  the  whole,  and  sim- 
ilarly situated  are  about  the  same  diagonal.! 

b.  If  a  body,  by  an  uniform  motion,  describe  one  side  of  a  paral- 
lelogram, in  the  same  time  that  it  would  describe  the  adjacent  side 
by  an  accelerative  force ;  this  body,  by  the  joint  action  of  these 
forces,  would  describe  a  curve,  terminating  in  the  opposite  angle 
of  the  parallelogram. 

Let  ABDc  be  a  parallelogram,  and  suppose  the  body  a  to  be 
carried  through  ab  by  an  uniform  force  in  the  a.  :e  K 


by  din  accelerative  force,  then  by  the  joint  action 
of  thi^e  forces,  the  body  would  describe  a  curve- 
agid.    For,  by  the  preceding  illustration,  if  the 


1 

other,  the  spaces  af,  fit.  and  hc,  will  be  in  the  same  proportion, 
and  the  line  agid  will  be  a  straight  line  when  the  body  is  acted 
upon  by  uniform  forces  ;  but  in  this  example  the  force  in  the  di- 
rection AB  being  uniform,  would  cause  the  body  to  move  over 
equal  spaces  ae,  el,  and  kb,  in  equal  portions  of  time ;  while  the 
accelerative  force  in  the  direction  ac,  would  cause  the  body  to 
describe  spaces  af,  fh,  and  hc,  increasing  in  magnitude  in  equal 


*  A  parallelogram  is  a  four-sided  figure,  having  its  opposite  sides  parallel,  and 
consequently  equal.    Euclid,  34  of  I. 
t  Euclid,  26  o/VI. 


Chap,  II. 


OF  THE  LAWS  OF  MOTION. 


67 


successive  portions  of  time  ;  hence  the  parallelograms  aegf,  AKm, 
&c.  are  not  about  the  same  diagonal*,  therefore  agid  is  not  a 
straight  line,  but  a  curve. 

6.  The  curvilinear  motions  of  all  the  planets  arise  from  the  uni- 
form projectile  forces  of  bodies  in  straight  lines,  and  the  universal 
power  of  attraction  which  draws  them  off  from  these  lines. 

If  the  body  e  be  projected  along 
the  straight  line  eaf,  in  free  space 
where  it  meets  with  no  resistance, 
and  is  not  drawn  aside  by  any  other 
force,  it  will  (by  the  first  law  of  mo- 
tion) go  on  forever  in  the  same  di- 
rection, and  with  the  same  velocity. 
For,  the  force  which  moves  it  from  e 
to  A  in  a  given  time,  will  carry  it  from 
A  to  f  in  a  successive  and  equal  por- 
tion of  time,  and  so  on ;  there  being 
nothing  either  to  obstruct  or  alter  its  motion.  But,  if,  when  the 
projectile  force  has  carried  the  body  to  a,  another  body  as  s,  be- 
gins to  attract  it,  with  a  power  duly  adjusted  and  perpendicular 
to  its  motion  at  a,  it  will  be  drawn  from  the  straight  line  eaf,  and 
revolve  about  s  in  the  circle^  agooa.  When  the  body  e  arrives 
at  o,  or  any  other  part  of  its  orbit,  if  the  small  body  m,  within  the 
sphere  of  e's  attraction,  be  projected,  as  in  the  straight  line  m  n, 
with  a  force  perpendicular  to  the  attraction  of  e,  it  will  go  round 
the  body  e,  in  the  orbit  m,  and  accompany  e  in  its  whole  course 
round  the  body  s.  Here  s  may  represent  the  sun,  e  the  earth, 
and  M  the  moon. 

If  the  earth  at  a  be  attracted  towards  the  sun  at  s,  so  as  to  fall 
from  A  to  H  by  the  force  of  gravity  alone,  in  the  same  time  which 
the  projectile  force  singly  would  have  carried  it  from  a  to  f  ;  by 
the  combined  action  of  these  forces  it  will  describe  the  curve  ag; 
and  if  the  velocity  with  which  e  is  projected  from  a,  be  such  as  it 
would  have  acquired  by  falling  from  a  to  v  (the  half  of  as)  by  the 
force  of  gravity  alonej,  it  will  revolve  round  s  in  a  circle. 


*  Euclid,  24  o/VI. 

f  If  any  body  revolve  round  another  in  a  circle,  the  revolving  body  must  be 
projected  with  a  velocity  equal  to  that  which  it  would  have  acquired  by  falling 
through  half  the  radius  of  the  circle,  towards  the  attracting  body.  Emerson^s  Cent. 
Forces,  Prop.  ii. 

X  A  body,  by  the  force  of  gravity  alone,  falls  16  1-12  feet  in  the  first  second  of 
time,  and  acquires  a  velocity  which  will  carry  it  uniformly  through  32  1-6  feet 
in  each  succeeding  second.  This  is  proved  experimentally  by  writers  on  me- 
chanics. 


68 


OP  THE  LAWS  OF  MOTION. 


Part  I. 


7.  If  one  body  revolve  round  another,  {as  the  earth  round  the 
sun,)  so  as  to  vary  its  distance  from  the  centre  of  motion,  the  pro- 
jectile and  centripetal  forces  must  each  he  variable,  and  the  path  of 
the  revolving  body  will  differ  from  a  circle* 

Thus,  if  while  a  projectile 
force  would  carry  a  planet  from 
A  to  p,  the  sun's  attraction  at  s 
would  bring  it  from  a  to  h,  the 
gravitating  power  would  be  too 
great  for  the  projectile  force ; 
the  planet,  therefore,  instead  of 
proceeding  in  the  circle  abc  (as 
in  the  preceding  article)  would 
describe  the  curve  ao,  and  ap- 
proach nearer  to  the  sun ;  so 
being  less  than  sa.  Now,  as  the 
centripetal  force,  or  gravitating 
power  always  increases  as  the 
square  of  the  planet's  distance 
from  the  sun  diminishesf ,  when 
the  planet  arrives  at  o  the  centripetal  force  will  be  increased, 
which  will  likewise  increase  the  velocity  of  the  planet,  and  ac- 
celerate its  motion  from  o  to  v ;  so  as  to  cause  it  to  describe  the 
arcs  OP,  QR,  RD,  DT,  TV,  succcssivcly  increasing  in  magnitude,  in 
equal  portions  of  time.  The  motion  of  the  planet  being  thus  ac- 
celerated, it  gains  such  a  centrifugal  force,  or  tendenc)^  to  fly  off 
at  V,  in  the  line  vw,  as  overcomes  the  sun's  attraction ;  this  cen- 
trifugal or  projectile  force  being  too  great  to  allow  the  planet  to 
approach  nearer  the  sun  than  it  is  at  v,  or  even  to  move  round 
the  sun  in  the  circle  t  ab  c  d,  &c.,  it  flies  off  in  the  curve  xzma, 
with  a  velocity  decreasing  as  gradually  from  v  to  a,  as  if  it  had 
returned  through  the  arcs  vt,  td,  dr,  &c.  to  a,  with  the  same 
velocity  which  it  passed  through  these  arcs  in  its  motion  from  a 
towards  v.  At  a  the  planet  will  have  acquired  the  same  velocity 
as  it  had  at  first,  and  thus  by  the  centrifugal  and  centripetal  forces 
it  will  continue  to  move  round  s. 


*  A  body  may  revolve  in  a  circle  by  means  of  a  variable  centripetal  force,  and 
with  a  variable  velocity,  but  the  centre  of  force  in  such  cases  cannot  bo  co-inci- 
dent with  the  centre  of  the  circle:  the  law  of  force  to  make  a  body  describe  the 
circumference  of  a  circle  with  a  variable  velocity,  about  a  centre  of  force  situated 
in  any  point  of  the  circle,  or  in  the  circumference  of  the  circle,  or  even  without  the 
circumference,  is  determined  by  Nevv^ton,  in  the  Seventh  Proposition  of  the  First 
Book  of  the  Principia. 

t  Newton's  Princip.  Book  III.  Prop.  ii. 


Chap,  II. 


OF  THE  LAWS  OF  MOTION. 


69 


Two  very  natural  questions  may  here  be  asked ;  viz.  why  the 
action  of  gravity,  if  it  be  too  great  for  the  projectile  force  at  o, 
does  not  draw  the  planet  to  the  sun  at  s  ?  and  why  the  projectile 
force  at  v,  if  it  be  too  great  for  the  centripetal  force,  or  gravity, 
at  the  same  point,  does  not  carry  the  planet  farther  and  farther 
from  the  sun,  till  it  is  beyond  the  power  of  his  attraction  ? 

First,  If  the  projectile  force  at  a  were  such  as  to  carry  the 
planet  from  a  to  g,  double  the  distance,  in  the  same  time  that  it 
w^as  carried  from  a  to  f,  it  would  require  four*  times  as  much 
gravity  to  retain  it  in  its  orbit,  viz.  it  must  fall  through  ai  in  the 
time  that  the  projectile  force  would  carry  it  from  a  to  g,  other- 
wise it  would  not  describe  the  curve  aop.  But  an  increase  of 
gravity  gives  the  planet  an  increase  of  velocity,  and  an  increase 
of  velocity  increases  the  projectile  force  ;  therefore,  the  tendency 
of  the  planet  to  fly  off  from  the  curve  in  a  tangent  p  m,  is  greater 
at  p  than  at  o,  and  greater  at  q  than  at  p,  and  so  on ;  hence,  while 
the  gravitating  power  increases,  the  projectile  power  increases, 
so  that  the  planet  cannot  be  drawn  to  the  sun. 

Secondly.  The  projectile  force  is  the  greatest  at,  or  near,  the 
point  V,  and  the  gravitating  power  is  likewise  the  greatest  at  that 
point.  For  if  as  be  double  of  vs,  the  centripetal  force  at  v  will 
be  four  times  as  great  as  at  a,  being  as  the  square  of  the  distance 
from  the  sun.  If  the  projectile  force  at  v  be  double  of  what  it 
w^as  at  a,  the  space  vw^  w^hich  is  the  double  of  af,  will  be  de- 
scribed in  the  same  time  that  af  w^as  described,  and  the  planet 
will  be  at  x  in  that  time.  Now,  if  the  action  of  gravity  had  been 
an  exact  counterbalance  for  the  projectile  force  during  the  time 
mentioned,  the  planet  would  have  been  at  t  instead  of  x,  and  it 
would  describe  the  circle  f,  a,  b,  c,  q-c;  but  the  projectile  force 
being  too  powerful  for  the  centripetal  force,  the  planet  recedes 
from  the  sun  at  s,  and  ascends  in  the  curve  xzm,  &c.  Yet,  it 
cannot  fly  off  in  a  tangent  in  its  ascent,  because  its  velocity  is  re- 
tarded, and  consequently  its  projectile  force  is  diminished,  by  the 
action  of  gravity.  Thus,  when  the  planet  arrives  at  z,  its  ten- 
dency to  fly  off  in  a  tangent,  z  n,  is  just  as  much  retarded,  by  the 
action  of  gravity,  as  its  motions  was  accelerated  thereby  at  q, 
therefore  it  must  be  retained  in  its  orbit.f 


*  Ferguson's  Astronomy,  Art.  153, 

t  Many  persons  are  at  a  loss  to  conceive  in  what  manner  the  alternative  access 
and  recess  of  the  earth  to  and  from  the  sun  can  be  reconciled  with  the  known 
law  of  centripetal  force,  which  increases  as  the  earth  approaches  the  sun,  and 
decreases  as  the  earth  recedes  from  the  sun :  thus,  the  action  of  the  sun  on  the 
earth  at  its  greatest  distance  is  the  least,  and  yet  it  is  able  to  draw  the  earth  from 
the  circular  orbit  passing  through  the  aphelion,  and  having  the  sun  in  the  centre  ; 
and  when  the  earth  is  nearest  to  the  sun,  and  the  centripetal  force  of  the  greatest 


70 


OF  THE  FIGURE  OP  THE  EAJITII,  &C. 


Pari  1. 


CHAPTER  III. 


Of  the  Figure  of  the  Earth,  and  its  Magnitude, 

The  figure  of  the  earth,  as  composed  of  land  and  water,  is 
nearly  spherical ;  the  proof  of  this  assertion  will  be  the  principal 
object  of  this  chapter.  The  ancients  held  various  opinions  respect- 
ing the  figure  of  the  earth  ;  some  imagined  it  to  be  cylindrical,  or 
in  the  form  of  a  drum ;  but  the  general  opinion  was  that  it  was  a 
vast  extended  plane,  and  that  the  horizon  was  the  utmost  limits 
of  the  earth,  and  the  ocean  the  bounds  of  the  horizon.  These 
opinions  were  held  in  the  infancy  of  astronomy;  and,  in  the  early 
ages  of  Christianity,  some  of  the  fathers  went  so  far  as  to  pro- 
nounce it  heretical  for  any  person  to  declare  that  there  was  such 
a  thing  as  the  antipodes.  But  by  the  industry  of  succeeding  ages, 
when  astronomy  and  navigation  were  brought  to  a  tolerable  de- 
gree of  perfection,  and  when  it  was  observed  that  the  moon  was 
frequently  eclipsed  by  the  shadow  of  the  earth,  and  that  such 
shadow  always  appeared  circular  on  the  disc  or  face  of  the  moon, 
in  whatever  position  the  shadow  was  projected,  it  necessarily  fol- 
lowed that  the  earth,  which  cast  the  shadow,  must  be  spherical  ; 
since  nothing  but  a  sphere,  when  turned  in  every  position  with 
respect  to  a  luminous  body,  can  cast  a  circular  shadow  ;  likewise 


value,  this  force  is  not  sufficient  to  retain  the  earth  at  the  perihelion  distance  in 
a  circular  orbit,  having  the  sun  in  the  centre  of  the  circle,  but  allows  it  to  recede 
from  the  sun,  and  ascend  towards  the  aphelion. 

When  the  earth,  or  a  planet,  describes  an  elliptical  orbit  about  the  sun  situated 
in  one  of  the  foci,  the  moving  body  endeavours  by  its  vis  inertiae  to  leave  the  orbit 
at  every  instant,  and  proceed  in  the  direction  of  the  tangent.  To  prevent  this 
escape,*  a  certain  force  directed  towards  the  sun,  must  be  continually  applied  to  the 
body  to  produce  a  continual  deflection  of  the  body  from  the  tangent  into  the  cur- 
vilinear path.  This  force  at  every  point  must  depend  on  the  curvature  of  the  orbit, 
estimated  in  the  direction  of  the  distance  to  the  sun  or  radius  vector,  and  on  the 
corresponding  velocity  of  the  moving  body,  with  respect  to  the  velocity  which  a 
body  must  have  to  describe  an  orbit  about  a  centre  of  force  in  free  space ;  it  is 
demonstrated  by  Newton  in  his  Principia,  Corollary  I.  to  Prop.  I.  that  the  velocity 
is  every  where  inversely  proportional  to  the  perpendicular  let  fall  on  the  tangent 
from  the  cerjtre  of  force.  In  this  manner  we  learn  that  the  velocity  of  the  body 
depends  on  the  position  of  the  body,  and  is  a  function  of  the  radius  vector,  the 
form  of  the  function  depending  on  the  nature  of  the  orbit.  This  velocity  or  func- 
tion of  the  distance  being  denoted  by  r,  the  central  force  must  increase  or  decrease 
as  V  increases  or  decreases,  when  the  curvation  is  the  same,  the  force  being  pro- 
portional to  t)^,  as  is  fully  proved  by  Newton,  and  many  subsequent  writers. 

Again,  where  the  curvature  is  greater,  the  force  must  be  greater  when  the  ve- 
locity is  the  same,  because  in  the  same  time  the  body  must  be  drawn  farther  from 
the  tangent,  in  the  ratio  of  the  curvature  ;  that  is  reciprocally  as  the  chord  of  cur- 
vature passing  through  the  centre  of  force.    This  chord  of  curvature,  vt^hich  we  may 


Chap.  III.  OF  THE  FIGURE  OF  THE  EARTH,  &C. 


71 


all  calculations  of  eclipses,  and  of  the  places  of  the  planets,  are 
made  upon  supposition  that  the  earth  is  a  sphere,  and  they  all 
answer  to  the  true  times,  when  accurately  calculated.  When  an 
eclipse  of  the  moon  happens,  it  is  observed  sooner  by  those  who 
live  eastward  than  by  those  who  live  westward  :  and,  by  frequent 
experience,  astronomers  have  determined  that,  for  every  fifteen 
degrees  difference  of  longitude,  an  eclipse  begins  so  many  hours 
sooner  in  the  easternmost  place,  or  later  in  the  westernmost.  If 
the  earth  were  a  plane,  eclipses  would  happen  at  the  same  time 
in  all  places,  nor  could  one  part  of  the  w^orld  be  deprived  of  the 
light  of  the  sun  while  another  part  enjoyed  the  benefit  of  it.  The 
Toyages  of  the  circumnavigators  sufliciently  prove  that  the  earth 
is  round  from  west  to  east.  The  first  who  attempted  to  circum- 
navigate the  globe  was  Magellan,  a  Portuguese,  who  sailed  from 
Seville  in  Spain  on  the  10th  of  August,  1519 ;  he  did  not  live  to 
return,  but  his  ship  arrived  at  St.  Lucar,  near  Seville,  on  the  7th 
of  September,  1522,  without  altering  its  direction,  except  to  the 
north  or  south,  as  compelled  by  the  winds,  or  intervening  land. 
Since  this  period,  the  circumnavigation  of  the  globe  has  been 


denote  by  ^,  is  also  a  function  of  the  radius  vector,  and  is  known  for  any  given 
curve.  Now  the  force  directed  to  the  focus,  in  which  the  sun  is  placed,  being  di- 
rectly as  v^,  and  inversely  as;?,  is  every  where  proportional  to  J^,  which  is  the  pro- 

P 

per  measure  of  the  central  force,  and  will  in  every  case  be  assignable  in  terms  of 
the  radius  vector  r.  From  this  reasoning  it  follows  that  whatever  be  the  nature  of 
the  curve,  and  the  situation  of  the  centre  offeree  in  the  plane  of  the  curve,  there  is 
at  every  point  of  the  curve  an  assignable  force  which  will  cause  a  body  to  describe 
the  curve. 

At  the  extremities  of  the  transverse  axis  of  the  elliptic  orbit,  the  curvature  is  the 
same,  so  that  if  v  and  v'  be  the  greater  and  less  velocities  at  the  perihelion 

and  aphelion,  the  two  forces  are  ~  and  ~,  which  because  p  is  common,  are  in 

the  ratio  of  to  v'^.  Now  let  r  and  i-'  be  the  perihelion  and  aphelion  distances, 
which  are  evidently  the  perpendiculars  from  the  centre  of  force  on  the  tangents ; 
and  therefore  by  the  general  rule  of  Newton  for  velocities,  we  have  v  :  V  : :  r'  :  r, 
and  therefore  :  v'^  'r^  :  ;  but  we  have  just  shown  that  if /and /'  denote  the 
forces  at  the  perihelion  and  aphelion,  we  have     :  v'^  : :  / consequently, 

/:/'::  r'^  : 

_1  \_ 
or/  :  /'  :  :        :  ; 

that  is,  the  forces  at  the  perihelion  and  aphelion  are  inversely,  as  the  squares  of  the 
distances.  It  is  evident  from  this  investigation,  that  the  inequality  of  the  forces  at 
the  ends  of  the  greater  axis,  arises  entirely  from  the  difference  in  the  velocities  at 
those  points.  If  the  velocities  were  equal,  the  central  forces  would  also  be  equal : 
and  if  it  can  be  shown  that  the  velocity  in  the  perihelion  is  greater  than  that  in  the 
aphelion,  it  follows  that  the  central  force  in  the  former  point  roust  be  greater  than 
that  in  the  latter. 


72 


OF  THE  FIGURE  OF  THE  EA'RTH,  SlC. 


Part  I. 


performed  at  different  times  by  Sir  Francis  Drake,  Lord  Anson, 
Captain  Cook,  &c.  The  voyages  of  the  circumnavigators  have 
been  frequently  adduced  by  writers  on  geography  and  the  globes, 
to  prove  that  the  earth  is  a  sphere ;  but  when  we  reflect  that  all 
the  circumnavigators  sailed  westward  round  the  globe,  (and  not 
northward  and  southward  round  it,)  they  might  have  performed 
the  same  voyages  had  the  earth  been  in  the  form  of  a  drum  or 
cylinder:  but  the  earth  cannot  be  in  the  form  of  a  cylinder,  for  if 
it  were,  then  the  difference  of  longitude  between  any  two  places 
would  be  equal  to  the  meridional  distance  between  the  same  places, 
and  on  a  Mercator's  chart,  which  is  contrary  to  observation. — 
Again,  if  a  ship  sail  in  any  part  of  the  world,  and  upon  any  course 
whatever,  on  her  departure  from  the  coast,  all  high  towers  or 
mountains  gradually  disappear,  and  persons  on  shore  may  see  the 
masts  of  the  ship  after  the  hull  is  hid  by  the  convexity  of  the  wa-, 
ter,  {see  Figure  III.  Plate  I.) — If  a  vessel  sail  northward,  in  north 
latitude,  the  people  on  board  may  observe  the  polar  star  gradu- 
ally to  increase  in  altitude  the  farther  they  go :  they  may  likewise 
observe  new  stars  continually  emerging  above  the  horizon  which 
were  before  imperceptible ;  and  at  the  same  time  those  stars 
which  appear  southv»'ard  will  continue  to  diminish  in  altitude  till 
they  become  invisible.  The  contrary  phenomena  v/ill  happen  if 
the  vessel  sail  southward,  hence  the  earth  is  spherical  from  north 
to  south,  and  it  has  already  been  shown  that  it  is  spherical  from 
east  to  west. 

The  arguments  already  adduced  clearly  prove  the  rotundity 
of  the  earth,  though  common  experience  shows  us  that  it  is  not 
strictly  a  geometrical  sphere ;  for  its  surface  is  diversified  with 
mountains  and  valleys :  but  these  irregularities  no  more  hinder 
the  earth  from  being  reckoned  spherical,  considering  its  magni- 
tude, than  the  roughness  of  an  orange  hinders  it  from  being  es- 
teemed round. ^ 

♦  Our  largest  globes  are  in  general  IS  inches  in  diameter,  and  the  diameter  of 
the  earth  is  about  7920  miles  ;  also  the  height  of  Chimbora90,  the  highest  mountain 
of  the  Andes  is  nearly  4  miles.  Now  to  find  on  a  globe  of  9  inches  radius,  an  ele- 
vation corresponding  to  Chimborafo  with  respect  to  the  earth  of  3960  miles  in 
radius, 

sayas  3960:  4::9  >^=^l^, 

and  therefore  an  elevation  of  the  _l_th  part  of  an  inch  on  the  surface  of  a  globe 
18  inches  in  diameter,  corresponds  to  the  altitude  of  Chimborafo  on  the  surface  of 

the  earth.  ^         ,       tt-  j  * 

The  highest  point  of  the  Himalaya  mountains  to  tne  north  ot  Hmdostan,  sur- 
veyed by  Capt.  Blake,  and  deduced  from  his  observations  by  Mr.  Colebrake,  is 
28015  feet  above  the  level  of  the  sea.  ,  ,r  , 

Edinburgh  Philosophical  Jonrml,  Vol.  V.  p.  40d. 


Chap.  III.       OP  THE  FIGURE  OF  THE  EARTH,  &C. 


73 


When  philosophical  and  mathematical  knowledge  arrived  at  a 
still  greater  degree  of  perfection,  there  seemed  to  be  a  very  suf- 
ficient reason  for  the  philosophers  of  the  last  age  to  consider  the 
earth  not  truly  spherical,  but  in  the  form  of  a  spheroid.*  This 
notion  first  arose  from  observations  on  pendulum  clocks,t  w^hich 
being  fitted  to  beat  seconds  in  the  latitudes  of  Paris  and  London, 
were  found  to  move  slower  as  they  approached  the  equator,  and 
at,  or  near  the  equator,  they  were  obliged  to  be  shortened  about 
}  of  an  inch  to  agree  with  the  times  of  the  stars  passing  the  me- 
ridian. This  difference  appearing  to  HuygensJ  and  Sir  Isaac 
Newton,  to  be  a  much  greater  quantity  than  could  arise  from  the 
alteration  by  heat  only,  they  separately  discovered  that  the  earth 
was  flatted  at  the  poles.§  By  the  revolution  of  the  earth  on  its 
axis,  (admitting  it  to  be  a  sphere)  the  centrifugal  force  at  the 
equator  would  be  greater  than  the  centrifugal  force  in  the  lati- 
tude of  London  or  Paris,  because  a  larger  circle  is  described  by 


*  A  spheroid  is  a  figure  formed  by  the  revohition  of  an  ellipsis  about  its  axis,  and 
an  ellipsis  is  a  curve-lined  figure  in  geometry,  formed  by  cutting  a  cone  or  cylinder 
obliquely  ;  but  its  nature  will  be  more  clearly  comprehended,  by  the  learner,  from 
the  following  description. 

Let  TR  (in  Plate  IV.  Figure  V.)  be  the  transverse  diameter,  or  longer  axis  of  the 
eUipsis,  and  co  the  conjugate  diameter,  or  shorter  axis.  With  the  distance  td  or 
DR  in  your  compasses,  and  c  as  a  centre,  describe  the  arc  Ff,  the  points  f,  f,  will  be 
the  two  foci  of  the  ellipsis.  Take  a  thread  of  the  length  of  the  transverse  axis  tr, 
and  fasten  its  ends  with  pins  in  f  and  f,  then  stretch  the  thread  Fif  and  it  will  reach 
to  I  in  the  curve ;  then  by  moving  a  pencil  round  with  the  thread,  and  keeping  it 
always  stretched,  it  will  trace  out  the  ellipsis  tcro.  If  this  ellipsis  be  made  to  re- 
volve on  its  longer  axis  tr,  it  will  generate  an  oblong  spheroid  or  Cassint's  figure  of 
the  earth ;  but  if  it  be  supposed  to  revolve  on  its  shorter  axis  co,  it  will  form  an  ob- 
late spheroid,  or  Sir  Isaac  Newton's  figure  of  the  earth.  The  orbits  or  paths  of  all 
the  planets  are  ellipses,  and  the  sun  is  situated  in  one  of  the  foci  of  the  earth's  orbit, 
as  will  be  observed  farther  on.  The  points  f,  f,  are  called  foci,  or  burning  points  ; 
because  if  a  ray  of  fight  issuing  from  the  point  f  meet  the  curve  in  the  point  i,  it  will 
be  reflected  back  into  the  focus  f  For  lines  drawn  from  the  two  foci  of  an  ellipsis 
to  any  point  in  the  curve,  make  equal  angles  with  a  tangent  to  the  curve  at  that 
point ;  and  by  the  laws  of  optics  the  angle  of  incidence  is  equal  to  the  angle  of  re- 
flection.   Rohertsori's  Conic  Sections,  Book  III.  Schofiura  to  Prop.  ix. 

t  Philosophical  Transactions,  No.  386. 

X  A  celebrated  mathematician  born  at  the  Hague  in  Holland,  in  1629. 

§  Supposing  the  earth  to  be  an  uniformly  dense  spheroid,  which  retains  its  figure 
by  the  equilibrium  of  its  gravity  and  centrifugal  force,  the  length  of  a  simple  pendu- 
lum vibrating  seconds  on  the  equator,  is  to  the  length  of  one  vibrating  in  the  same 
time  at  the  pole,  as  the  axis  of  the  earth  to  its  equatorial  diameter ;  and  the  increase 
of  length  in  any  latitude  above  the  length  at  the  equator,  is  as  the  square  of  the  sine 
of  the  latitude,  as  was  first  demonstrated  by  Sir  Isaac  Newton,  and  afterwards  by 
other  authors.  But  the  figure  of  the  earth,  as  given  by  Newton,  was  derived  from 
the  improbable  hypothesis  of  uniform  density,  and  therefore  cannot  be  safely  em- 
ployed in  determining  by  calculation  the  length  of  a  seconds  pendulum  in  different 
latitudes.    A  different  method  has  been  adopted  by  philosophers,  which  consists  in 

10 


74 


OF  THE  FIGURE  OF  THE  EARTH,  &C. 


Part  L 


the  equator,  in  the  same  time ;  but  as  the  centrifugal  force  (or 
tendency  which  a  body  has  to  recede  from  the  centre)  increases, 
the  action  of  gravity  necessarily  diminishes :  and  where  the  ac- 
tion of  gravity  is  less,  the  vibrations  of  pendulums  of  equal  lengths 
become  slower  :  hence,  supposing  the  earth  to  be  a  sphere,  we 
have  two  causes  why  a  pendulum  should  move  slower  at  the  equa- 
tor than  at  London  or  Paris,  viz.  the  action  of  heat,  which  dilates 
all  metals,  and  the  diminution  of  gravity.  But  these  two  causes 
combined  would  not,  according  to  Sir  Isaac  Newton,  produce  so 
great  a  difference  as  \  of  an  inch  in  the  length  of  a  pendulum  ;  he 
therefore  supposed  the  earth  to  assume  the  same  figure  that  a  ho- 
mogeneous fluid  would  acquire  by  revolving  on  an  axis,  viz.  the 
figure  of  an  oblate  spheroid,  and  found  that  the  "  diameter  of  the 
earth  at  the  equator,  is  to  its  diameter  from  pole  to  pole,  as  230  to 
229."*  Notwithstanding  the  deductions  of  Sir  Isaac  Newton,  on 
the  strictest  mathematical  principles,  many  of  the  philosophers  in 
France,  the  principal  of  whom  was  Cassinif ,  asserted  that  the 


deducing  the  measure  of  gravity  at  every  point  of  the  earth's  surface,  from  a  select 
number  of  observations  made  at  different  points  of  the  meridian. 

According  to  this  method,  if  the  gravity  at  the  equator  be  denoted  by  unity,  that 
at  the  pole  will  be  expressed  by  1.005515  ;  and  in  any  latitude  the  gravity  will  be 
measured  by  1  -f-  005515  sin 

Thus,  in  latitude  30^  we  have  X  =  30°,  sin.  X  =  ^,  and  sin.  ^X  =  4,  whence 
1  +  005515  sin.  ^X  =  1.001379. 

In  latitude  45°,  we  have  sin.      =  |,  and  thus  1  -f-  005515  sin.  ^X  =  1.002757. 

In  general,  if  the  length  of  a  seconds  pendulum  at  the  equator  be  denoted  byp, 
and  if  tt  be  the  length  of  any  latitude  X)  we  have  for  determining  cj(  the  following 
equation : 

^  =  _p  (1+005515  sin.  ^a) 
See  on  this  subject  the  transactions  of  the*^7n.  Phil.  Soc.  Vol.  I.  J^ew  Series,  pub- 
lished in  1818. 

*  The  ratio  of  229  to  230,  which  Newton  obtained,  for  that  of  the  axis  of  the 
earth  to  its  equatorial  diameter,  was  deduced  from  the  supposition  of  uniform  den- 
sity in  the  earth.    It  is  necessary  in  determining  this  figure,  to  have  recourse  to 
methods  which  are  not  hable  to  such  uncertainty  :  by  these  it  is  known  that  the 
ratio  of  the  axis  of  the  earth  to  the  diameter  of  the  equator,  is  nearly  that  of  319  to 
320  ;  that  the  semi-axis  is  nearly   3951.09  E.  miles. 
The  equatorial  semi-diameter    -  3963.48 
The  difference  of  which  is         -  12.39 
And  the  mean  semi-diameter  is  -  3959.35 

The  earth  being  taken  as  a  sphere,  the  mean  semi-diameter  is  the  radius  of  the 
sphere.  If  a  sphere  of  18  inches  diameter  were  compressed  towards  the  poles  and 
elevated  towards  the  equator,  so  as  to  become  similar  in  figure  to  the  earth,  the 
difference  of  the  semi-diameter  would  be  nearly  -g-lg-  =  -jy^h  part  of  an  inch, 
which  is  too  small  a  quantity  to  be  introduced  in  the  construction  of  such  bodies 
intended  to  exhibit  a  representation  of  the  earth. 

t  Son  of  the  celebrated  Italian  astrotiomer;  he  was  born  at  Parts  in  1677. 


Chap.  III.       OF  THE  FIGURE  OF  THE  EARTH,  &C. 


75 


earth  was  an  oblong  spheroid,  the  polar  diameter  being  the  longer  : 
and  as  these  different  opinions  were  supposed  to  retard  the  gen- 
eral progress  of  science  in  France,  the  king  resolved  that  the  affair 
should  be  determined  by  actual  admeasurement  at  his  own  expense. 
Accordingly,  about  the  year  1735,  two  companies  of  the  most  able 
mathematicians  of  the  nation  were  appointed  ;  the  one  to  measure 
the  degree  of  a  meridian  as  near  to  the  equator  as  possible,  and 
the  other  company  to  perform  alike  operation  as  near  the  pole  as 
could  be  conveniently  attempted.  The  results  of  these  admeas- 
urements contradicted  the  assertions  of  Cassini,  and  of  J.  Bernou- 
illi,  (a  celebrated  mathematician  of  Basil  in  Switzerland,  who 
warmly  espoused  his  cause,)  and  confirmed  the  calculations  of  Sir 
Isaac  Newton.  In  the  year  1756,  the  Royal  Academy  of  Scien- 
ces of  Paris  appointed  eight  astronomers  to  measure  the  length 
of  a  degree  between  Paris  and  Amiens :  the  result  of  their  ad- 
measurement gave  57069  toises  for  the  length  of  a  degree. 

The  utility  of  finding  the  length  of  a  degree  in  order  to  deter- 
mine the  magnitude  and  figure  of  the  earth,  may  be  rendered  fa- 
miliar to  the  learner  thus :  suppose  1  find  the  latitude  of  London 
to  be  51^°  north,  and  travel  due  north  till  I  find  the  latitude  of  a 
place  to  be  5^|°  north,  I  shall  then  have  travelled  a  degree,  and 
the  distance  between  the  two  places,  accurately  measured,  will 
be  the  length  of  a  degree :  now  if  the  earth  be  a  correct  sphere, 
the  length  of  a  degree  on  a  meridian,  or  a  great  circle,  will  be 
equal  all  over  the  w^orld,  after  proper  allowances  are  made  for  el- 
evated ground,  &c. :  the  length  of  a  degree  multiplied  by  360 
will  give  the  circumference  of  the  earth,  and  hence  its  diameter, 
&c.  will  be  easily  found  :  but  if  the  earth  be  any  other  figure  than 
that  of  a  sphere,  the  length  of  a  degree  on  the  same  meridian  will 
be  different  in  different  latitudes,  and  if  the  figure  of  the  earth  re- 
semble an  oblate  spheroid,  the  lengths  of  a  degree  will  increase  as 
the  latitudes  increase.  The  English  translation  of  Maupertuis's 
figure  of  the  earth,  concludes  with  these  words :  {see  page  163  of 
the  work  :)  "  The  degree  of  the  meridian  which  cuts  the  polar  circle 
being  longer  than  the  degree  of  a  meridian  in  France,  the  earth  is 
a  spheroid  flatted  towards  the  poles  T  For,  the  longer  a  degree  is, 
the  greater  must  be  the  circle  of  which  it  is  a  part ;  and  the  greater 
the  circle  is,  the  less  is  its  curvature. 

The  first  person  who  measured  the  length  of  a  degree  with  any 
appearance  of  accuracy,  was  Mr.  Richard  Norwood :  by  measur- 
ing the  distance  between  London  and  York,  he  found  the  length 
of  a  degree  to  be  367196  English  feet,  or  69^  English  miles; 
hence,  supposing  the  earth  to  be  a  sphere,  its  circumference  will 


76 


or  THE  FIGURE  OF  THE  EARTH,  &C. 


Part  I. 


be  25020  miles,  and  its  diameter  7964*  miles  ;  but  if  the  length 
of  a  degree  at  a  medium,  be  57069  toises,  the  circumference  of 
the  earth  will  be  24873  English  miles,  its  diameter  7917  miles, 
and  the  length  of  a  degree  Q^^q  miles.f 

Conclusion.  Notwithstanding  all  the  admeasurements  that 
have  hitherto  been  made,  it  has  never  been  demonstrated,  in  a 
satisfactory  manner,  that  the  earth  is  strictly  a  spheroid  ;  indeed, 
from  observations  made  in  different  parts  of  the  earth,  it  appears 
that  its  figure  is  by  no  means  that  of  a  regular  spheroid,  nor  that 
of  any  other  known  regular  mathematical  figure,  and  the  only  cer- 
tain conclusion  that  can  be  drawn  from  the  works  of  the  several 
gentlemen  employed  to  measure  the  earth,  is,  that  the  earth  is 
something  more  flat  at  the  poles  than  at  the  equator.  The  course  of 
a  ship,  considering  the  earth  a  spheroid,  is  so  near  to  what  it 
would  be  on  a  sphere,  that  the  mariner  may  safely  trust  to  the 
rules  of  globular  sailingj,  even  though  his  course  and  distance 
were  much  more  certain  than  it  is  possible  for  them  to  be.  For 
which,  and  similar  reasons,  mathematicians  content  themselves 
with  considering  the  earth  as  a  sphere  in  all  practical  sciences, 
and  hence  the  artificial  globes  are  made  perfectly  spherical,  as 
the  best  representation  of  the  figure  of  the  earth. 


*  5280  feet  make  a  mile,  therefore  367196  divided  by  5280  gives  69^  miles  nearly, 
which  multiplied  by  360  produces  25020  miles,  the  circumference  of  the  earth  ;  but 
the  circumference  of  a  circle  is  to  its  diameter  as  22  to  7,  or  more  nearly  as  355  to 
113;  hence  355:  113::  25020  miles:  7964  miles,  the  diameter  of  the  earth. 
Again,  6  French  feet  make  1  toise,  therefore  57069  toises  are  equal  to  342414 
French  feet ;  but  107  French  feet  are  equal  to  114  English  feet,  hence  107  F.  f.  : 
114  E.  f.  :  :  342414  F.  f.  :  364814  English  ft.  which  divided  by  5280,  the  feet  in  a 
mile,  gives  69.09  miles,  the  length  of  a  degree  by  the  French  admeasurement.  Or, 
342414  multiplied  by  360  produces  123269040  French  feet,  the  circumference  of  the 
earth,  and  107  :  114  :  :  123269040  :  131333369  English  feet,  equal  to  24873.74  miles, 
the  circumference  of  the  earth,  and  355  :  113:  :24873.74  :  7917  miles,  the  diameter 
of  the  earth. 

t  The  length  of  a  degree  in  lat.  51^  9'  N.  is  364950  feet  =  69.12  Enghsh  miles. 
Trigonometrical  survey  of  England  and  Wales,  Vol.  11.  Part  II.  page^l  13.  Mr, 
Swanberg,  a  Swedish  mathematician,  found  the  length  of  a  degree  to  be  57196.159 
toises  =  365627.782  Enghsh  feet  =  69.247  miles. 

X  Robertson's  Navigation,  Book  VIII.  Art.  143. 


Chap,  IV.         DIURNAL  AND  ANNUAL  MOTION,  (fec. 


77 


CHAPTER  IV. 

Of  the  Diurnal  and  Annual  Motion  of  the  Earth. 

The  motion  of  the  earth  was  denied  in  the  early  ages  of  the 
world,  yet  as  soon  as  astronomical  knowledge  began  to  be  more 
attended  to,  its  motion  received  the  assent  of  the  learned,  and  of 
such  as  dared  to  think  differently  from  the  multitude,  or  were  not 
apprehensive  of  ecclesiastical  censure.  The  astronomers  of  the 
last  and  present  age  have  produced  such  a  variety  of  strong  and 
forcible  arguments  in  favour  of  the  motion  of  the  earth,  as  must 
effectually  gain  the  assent  of  every  impartial  inquirer. — Among 
the  many  reasons  for  the  motion  of  the  earth,  it  will  be  sufficient 
to  point  out  the  following : 

1.  Of  the  Diurnal  Motion  of  the  Earth. 

The  earth  is  a  globe  of  7920  miles  in  diameter,  (as  has  been 
shown  in  Chap.  III.)  and  by  revolving  on  its  axis  every  23  h.  56 
min.  4  sec.  from  west  to  east,  it  causes  an  apparent  diurnal  motion 
of  all  the  heavenly  bodies  from  east  to  west.  We  need  only  look 
at  the  sun,  or  stars,  to  be  convinced,  that  either  the  earth,  which 
is  no  more  than  a  point*  when  compared  with  the  heavens,  re- 
volves on  its  axis  in  a  certain  time,  or  else  the  sun,  stars,  <fec.  re- 
volve round  the  earth  in  nearly  the  same  time.  Let  us  suppose 
for  instance  that  the  sun  revolves  round  the  earth  in  24  hours,  and 
that  the  earth  has  no  diurnal  motion.  Now,  it  is  a  known  princi- 
ple in  the  laws  of  motion,  that  if  any  body  revolve  round  another 
as  its  centre,  it  is  necessary  that  the  central  body  be  always  in  the 
plane  in  which  the  revolving  body  moves,  whatever  curve  it  de- 
scribes ;f  therefore  if  the  sun  move  round  the  earth  in  a  day,  its 
diurnal  path  must  always  describe  a  circle  which  will  divide  the 
earth  into  two  equal  hemispheres.  But  this  never  happens  except 
on  tv^'o  days  of  the  year,  viz.  at  the  time  of  the  equinoxes,  when 
the  sun  rises  exactly  in  the  east,  and  sets  exactly  in  the  west. 
For,  from  the  2ist  of  March  to  the  23d  of  "September,  the  sun 
rises  to  the  north  of  the  east,  and  sets  to  the  north  of  the  west ; 
and  from  the  23d  of  September  to  the  21st  of  March,  it  rises  to  the 
south  of  the  east  and  sets  to  the  south  of  the  west,  and  therefore 
its  diurnal  path  divides  the  globe  into  two  unequal  parts  ;  conse- 


*  Dr.  Keill,  Lect.  26.  |  Emerson's  Astronomy,  p.  11. 


78 


OF  THE  DIURNAL  AND  ANNUAL 


Part  1. 


quently  the  sun  does  not  move  round  the  earth.  To  render  this 
more  intelligible  to  a  young  student,  let  a  pin,  of  some  inches  in 
length,  be  fixed  perpendicularly  upon  an  horizontal  plane,  and  ob- 
serve the  shadow  that  the  top  of  it  describes  on  any  day  of  the 
year ;  this  shadow  will  always  be  a  curve,  except  at  the  time  of 
the  equinoxes,  hence  the  earth  is  never  in  the  sun's  apparent  diur- 
nal orbit  but  then  ;  for  if  the  top  of  the  pin  kept  all  the  time  in  the 
plane  of  the  sun's  apparent  diurnal  orbit,  the  shadow  described 
would  be  a  straight  line,*  because  it  would  fall  in  the  intersection 
of  two  planes  ;|  therefore  the  sun  has  no  diurnal  motion  round 
the  earth,  consequently  the  earth  has  a  diurnal  motion  on  its  axis. 

It  is  no  argument  against  the  earth's  diurnal  motion,  that  we  do 
not  feel  it ;  a  person  in  the  cabin  of  a  ship,  on  smooth  water,  can- 
not perceive  the  ship's  motion  when  its  turns  gently  and  uniformly 
round  ;J  neither  does  the  earth  cause  bodies  to  fall  from  its  sur- 
face ;  for  all  bodies,  of  whatever  matter  they  are  composed,  are 
drawn  to  the  earth  by  the  power  of  its  central  attraction  ;§  which, 
laying  hold  of  them  according  to  their  densities,  or  quantities  of 
matter,  without  regard  to  their  magnitudes,  constitutes  what  we 
call  weight. 

The  phsenomena  of  the  apparent  diurnal  motion  of  the  sun  may 
be  explained  by  the  motion  of  the  earth  ;  thus,  let  ifgh  {Plate 
l.fig.  Y.)  represent  the  earth,  s  the  sun,  and  the  circle  dsbc  the 
apparent  concavity  of  the  heavens.  Let  the  earth  revolve  on 
its  axis  from  i  towards  g  (viz.  from  west  to  east).  Suppose  a 
spectator  to  be  at  i,  the  sun,  which  is  at  an  immense  distance,  and 
enlightens  half  the  globe  at  once,  will  appear  to  be  rising.  As 
the  earth  moves  round,  the  spectator  is  carried  towards  f,  and 
the  sun  seems  to  increase  in  height ;  when  he  has  arrived  at  f, 
the  sun  is  at  the  highest.  As  the  earth  continues  to  turn  round, 
the  spectator  is  carried  from  f  towards  g,  and  the  altitude  of  the 
sun  keeps  continually  diminishing ;  when  he  has  arrived  at  g, 
the  sun  is  setting.  During  the  time  the  spectator  has  been  car- 
ried from  I  to  G,  the  sun  has  appeared  to  move  the  contrary  way. 
Hence  it  is  evident  that  while  the  spectator  is  carried  through  the 
illuminated  half  of  the  earth,  it  is  day-light ;  at  the  middle  point 


*  Emerson's  Dialling,  Prop.  II.  p.  9th. 

tit  is  demonstrated  in  Euclid,  Prop.  III.  Book  XL,  and  in  Keith's  Geometry, 
Prop.  III.  Book  IX.,  that  if  two  planes  intersect  each  other,  their  common  section 
is  a  straight  line. 

X  Ferguson's  Astronomy,  Art.  119. 

§  Newton's  Principia,  Book  III.  Prop.  vii. 


Chap.  IV. 


MOTION  OF  THE  EARTH. 


79 


F,  it  is  noon ;  also  while  he  is  carried  through  the  dark  hemis- 
phere, it  is  night ;  and  at  h  it  is  midnight.  Thus  the  vicissitude 
of  day  and  night  evidently  appears  by  the  rotation  of  the  earth 
about  its  axis:  vs^hat  has  been  said  of  the  sun  is  equally  applicable 
to  the  moon,  or  any  star  placed  at  s ;  therefore  all  the  celestial 
bodies  seem  to  rise  and  set  by  turns,  according  to  their  various 
situations.  The  spectator  at  i,  f,  g,  h,  w'lW  alw^ays  have  his  feet 
towards  the  centre  of  the  earth,  and  the  sky  above  his  head,  what- 
ever position  the  earth  may  have  ;  agreeably  to  the  laws  of  gravi- 
tation or  attraction.  Thus  an  inhabitant  at  a  will  be  the  most 
powerfully  attracted  towards  his  antipodes  6,  because  there  is 
the  greatest  mass  of  earth  under  his  feet  in  that  direction  ;  for 
the  same  reason  h  will  be  the  most  attracted  towards  a,  m,  to- 
wards n,  and  n  towards  m,  &c. ;  hence  it  appears  that  every  body 
on  the  surface  of  the  earth  is  attracted  towards  its  centre,  or 
rather  towards  the  antipodes  of  that  body,  for  the  whole  earth  is 
the  attracting  mass,  and  not  some  unknown  substance  placed  in 
the  centre  of  the  earth.  There  is  no  such  thing  as  an  upper  and 
under  side  of  the  earth :  suppose  a  to  be  an  inhabitant  of  Nankin 
in  China,  h  will  be  an  inhabitant  of  South  America  near  Buenos 
Ayres,  each  having  the  earth  under  his  feet  and  the  sky  above 
his  head  ;  also  if  n  be  an  inhabitant  a  little  east  of  Quito  in  South 
America,  on  the  equator,  m  will  be  an  inhabitant  upon  the  equator 
in  the  island  of  Sumatra,  and  in  the  course  of  12  hours  n  will 
have  the  same  position  as  m,  by  the  revolution  of  the  earth. 

2.  Of  the  Annual  Motion  of  the  Earth, 

The  diurnal  revolution  of  the  earth  on  its  axis  being  proved, 
the  annual  motion  round  the  sun  will  be  readily  admitted ;  for, 
either  the  earth  moves  round  the  sun  in  a  year,  or  else  the  sun 
moves  round  the  earth  ;  now,  by  the  laws  of  centripetal  force,  if 
two  bodies  revolve  about  each  other,  they  revolve  round  their 
common  centre  of  gravity  ;*  and  it  is  evident,  that  if  the  two 
bodies  be  of  an  equal  magnitude  and  density,  the  centre  of  gravity 
will  be  equi-distant  from  each  body ;  but,  if  they  be  of  different 
masses,  the  centre  of  gravity  will  be  nearest  to  the  larger  body ; 
if  the  earth,  therefore,  remain  in  the  same  situation  while  the  sun 
revolves  round  it,  its  mass  must  be  much  greater  than  that  of  the 
sun  ;  for  it  is  contrary  to  the  laws  of  nature  for  a  heavy  body  to 


*  The  centre  of  gravity  of  two  bodies  is  a  point,  on  which,  if  they  were  both  sup- 
ported by  a  straight  line  joining  their  centres,  they  would  rest  in  equilibrium. 


80 


OF  THE  DIURNAL  AND  ANNUAL 


Part  1. 


revolve  round  a  light  one  as  its  centre  of  motion :  but  from  obser- 
vations on  the  dimensions*  and  distances  of  the  sun  and  planets, 
it  appears  that  the  sun  so  greatly  exceeds,  not  only  the  earth,  but 
the  planets,  in  mass,  that  the  common  centre  of  gravity  of  the 
whole  is  almost  constantly  within  the  body  of  the  sun,  so  that  the 
sun's  motion  round  the  common  centre  of  gravity  of  the  earth  and 
the  planets  is  not  perceptible  by  ordinary  observers.  Not  only 
the  earth,  therefore,  but  the  planets,  move  round  the  sun. 

It  is  also  evident  that  the  motion  of  the  earth  in  its  orbit  is  from 
west  to  east,  for  if  the  sun  be  observed  to  rise  with  any  fixed 
star,  which  is  near  the  ecliptic,  it  will,  in  the  course  of  a  few  days, 
appear  to  the  eastward  of  that  star.  And  in  the  period  of  a  year 
it  will  arrive  at  the  same  star  again. 

The  earth  is  computed  to  be  95  millions  of  miles  from  the  sun^f 
and  performs  its  revolution  round  him,  described  an  elliptical 
orbit  or  path,J  in  365  days  5  hours  48  minutes  and  48  seconds, 
from  any  equinox  or  solstice  to  the  same  again  ;  it  travels  at  the 


♦  The  apparent  diameters  of  the  planets  are  found  by  a  micrometer  placed  in  the 
focus  of  a  telescope,  or,  the  apparent  diameter  of  the  sun  may  be  measured  by 
means  of  the  projection  of  his  image  into  a  dark  room,  through  a  circular  aperture. 
From  these  apparent  diameters,  and  the  respective  distances  from  the  earth,  the 
real  diameters  of  the  sun  and  planets  may  be  determined. 

f  In  Plate  IV.  Fig.  vi.  let  o  be  the  centre  of  the  earth,  p  the  place  of  an  observer 
on  its  surface,  and  s  the  sun  or  a  planet  in  the  heavens :  now  to  an  observer  at  o, 
the  sun  would  appear  at  a,  and  to  an  observer  at  p  it  would  appear  at  h ;  the  arc 
a  b,  or  the  angle  a  s  b  which  is  equal  to  the  angle  pso,  is  called  the  horizontal  paral- 
lax. Mr.  Short,  in  vol.  52.  part  ii.  of  the  Philosophical  Transactions,  has  deter- 
mined the  horizontal  parallax  of  the  sun  to  be  8".65,  at  its  mean  distance  from  the 
earth.    Hence,  by  trigonometry, 

Logarithmical  sine  of  8". 65,  or  angle  pso  -  -  5.6319140 
Is  to  one  semi-diameter  of  the  earth  po  -         -  0.0000000 

As  radius,  sine  of  90  decrees,  or  sine  of  0P3  -  -  10.0000000 
Is  to  23S8-2.84  semi-diameters  ...  -  4.3780860 
Now  if  we  take  the  diameter  of  the  earth  7970  miles,  as  Mr.  Short  has  done,  the 
semi-diameter  3985  multiphed  by  23882.84  gives  95173117  miles,  the  distance  of 
the  earth  from  the  sun  :  if  the  diameter  of  the  earth  be  taken  7964  miles,  the  dis- 
tance will  be  95101468  miles  ;  if  it  be  taken  7917  miles,  (see  the  chapter  of  the 
Figure  of  the  Earth),  the  distance  will  be  94540222  miles.  In  a  case  of  such  un- 
certainty, where  a  very  small  error  in  the  parallax  will  produce  an  astonishing  dif- 
ference in  the  conclusion  of  the  process,  and  where  an  error  in  the  diameter  of  the 
earth  will  also  affect  the  operation,  we  may  rest  content  with  estimating  the  dis- 
tance of  the  earth  from  the  sun  at  95  milUons  of  miles.  Mr.  IVoodhouse,  in  his  As- 
tronomy, page  384,  calculates  the  sun's  horizontal  parallax  to  be  8''.7017,  and  at 
page  284,  where  he  has  given  the  distances  of  the  planets  from  the  sun  according 
to  Laplace,  he  states  the  distance  of  the  earth  from  the  sun  to  be  93726900  miles. 

\  The  idea  that  the  earth  moved  in  an  elliptical  orbit  was  first  conceived  by  Kep- 
ler, an  eminent  German  astronomer,  and  demonstrated  by  Sir  Isaac  Newton.  See 
the  Principia,  Book  III.  Prop,  xiii. 


Chap.  IV. 


MOTION  OP  THE  EARTH. 


81 


rate  of  upwards  of  68,000  miles  per  hour.*  Besides  this  motion, 
which  is  common  to  every  inhabitant  of  the  earth,  the  inhabitants 
at  the  equator  are  carried  1042f  miles  every  hour  by  the  diurnal 
revolution  of  the  earth  on  its  axis,  while  those  in  the  parallel  of 
London  are  carried  only  about  644  miles  per  hour.  The  lixis 
of  the  earth  makes  an  angle  of  23^  28  with  a  perpendicular  to 
the  plane  of  its  orbit,  and  keeps  always  the  same  oblique  direc- 
tion throughout  its  annual  course  J  ;  hence  it  follows,  that,  during 
one  part  of  its  course,  the  north  pole  is  turned  towards  the  sun, 
and,  during  another  part  of  its  course,  the  south  pole  is  turned 
towards  it  in  the  same  proportion  ;  which  is  the  cause  of  the  dif- 
ferent seasons,  as  spring,  summer,  autumn,  and  winter.  The  or- 
bit of  the  earth  being  elliptical,  the  earth  must  at  some  times  ap- 
proach nearer  to  the  sun  than  at  others,  and  will  of  course  take 
more  time  in  moving  through  one  part  of  its  path  than  through 
another.  Astronomers  have  observed  that  the  earth  is  more 
rapid  in  the  winter  half  of  its  orbit  than  in  the  summer,  by  about 
seven  days ;  {see  the  note  to  the  6th  Geographical  Theorem,  p.  59;) 
but  although  in  the  winter  we  are  nearer  to  the  sun  than  in  the 
summer,  yet  in  that  season  it  seems  farthest  from  us,  and  the 
weather  is  more  cold  and  inclement ;  the  simple  account  of 
which  phsenomenon  is,  that  the  sun's  rays  falling  more  perpen- 
dicularly on  us  in  summer,  augment  the  heat  of  the  weather ;  so, 
being  transmitted  more  obliquely  on  our  parallel  of  latitude  dur- 
ing the  winter,  the  cold  is  increased  and  rendered  more  intense. 
Besides,  the  days  are  longer  in  summer  than  in  winter,  on  which 
account  the  heat  of  summer  is  still  farther  augmented.  The  heat 
in  the  torrid  zone  does  not  arise  from  those  parts  of  the  earth 
being  nearer  to  the  sun,  but  from  the  rays  of  the  sun  falling  per- 
pendicular upon,  and  darting  immediately  through  the  atmos- 


*  The  earth's  distance  from  the  sun  is  95  millions  of  miles,  the  mean  diameter 
of  its  orbit  is  therefore  190  millions  of  miles,  and  the  circumference  of  a  circle  is 
three  times  the  diameter  and  one  seventh  more ;  or  the  circumference  is  to  the 
diameter  as  355  to  113  more  nearly  ;  hence  113  :  355  :  :  190,000,000  :  596902654, 
the  circumference  of  the  orbit ;  but  this  circumference  is  described  in  365  days  5 
hours  48  minutes  48  seconds,  or  365  days  6  hours  nearly,  or  8766  hours  ;  hence 
8766  h.  :  596902654  m.  :  :  1  h.  :  68092  miles  per  hour  the  inhabitants  of  the  earth 
are  carried  by  its  annual  revolution. 

1  These  distances  are  found  by  multiplying  the  number  of  miles  contained  in  a 
degree  in  any  parallel  of  latitude  by  15  ;  thus  the  circumference  of  the  earth  at  the 
equator  is  360"  X  69^  m.  and  in  the  latitude  of  London  it  is  equal  to  360  X  42.95, 
and  24  h.  :  360°  X  69^  :  :  1  h.  :  1042^  m. ;  or  1  :  15  X  69^  :  :  1  :  1042^  m. 

X  This  is  not  strictly  true,  though  the  variation,  called  the  nutation  of  the  earth's 
axis,  is  scarcely  perceptible  in  two  or  three  years.   Keitl,  Lect.  viii. 


82 


OF  THE  DIURNAL  AND  ANNUAL. 


Part  L 


phere.  It  might  likewise  be  expected  that,  as  we  are  less  distant 
from  the  sun  in  the  winter  than  in  the  summer,  it  would  appear 
larger ;  but  the  difference  of  situation  is  so  small  as  to  make  no 
sensible  alteration  in  the  sun's  apparent  magnitude. 

l*he  sun  is  not  supposed  to  be  fixed  in  the  centre  of  the  earth's 
elliptical  orbit,  but  in  one  of  the  foci.  Let  s  represent  the  sun 
{Plate  II.  Fig.  3.)  and  agfbde  the  elliptical  orbit  of  the  earth. 
Then  a  is  called  the  Perihelion,  or  lower  apsis,  being  the 
earth's  nearest  distance  from  the  sun  ;  b  is  called  the  Aphelion,  or 
higher  apsis,  being  the  greatest  distance  of  the  earth  from  the 
sun,  and  sc  the  distance  between  the  sun  (in  the  focus)  and  the 
centre,  is  called  the  eccentricity  of  the  earth's  orbit.  If  from  the 
centre  c  there  be  erected  upon  the  axis  ab  the  perpendicular  ce, 
meeting  the  orbit  in  e,  and  the  line  se  be  drawn,  it  will  represent 
the  mean  distance  of  the  earth  from  the  sun,  being  equal  to  half 
the  axis  ab*,  consequently  se  is  95  millions  of  miles. 

Though  the  motion  of  the  earth  in  its  orbit  be  not  uniform,  yet 
it  is  regulated  by  a  certain  immutable  law,  from  which  it  never 
deviates  ;  which  is,  that  a  line  drawn  from  the  centre  of  the  sun  to 
the  centre  of  the  earth,  being  carried  about  with  an  angular  mo- 
tion, describes  an  elliptical  area  proportional  to  the  time  in  which 
that  area  is  describedf ,  viz.  if  the  times  in  which  the  earth  moves 
from  A  to  E,  from  e  to  d,  and  from  d  to  b,  be  equal,  then  the  areas, 
or  spaces,  ase,  esd,  and  dsb,  will  all  be  equal.  The  motion  of 
the  earth  is  sometimes  quicker  and  sometimes  slower  in  moving 
through  equal  parts  of  its  orbit ;  for  when  the  earth  is  at  a  (in 
the  winter)  the  sun  attracts  it  more  strongly,  and  therefore  the 
motion  is  quicker  than  any  where  else  ;  likewise,  when  it  is  at  b 
(in  the  summer)  it  is  least  affected  by  the  sun's  attraction,  and 
consequently  the  motion  there  is  slower  than  in  any  other  part  of 
its  orbit,  for  the  power  of  gravity  decreases  as  the  square  of  the 
distance  increases  J ;  besides  it  is  obvious,  from  the  construction 
of  the  figure,  that,  if  the  space  ase  be  described  in  the  same  time 
with  the  space  bsd,  the  arc  ae  will  be  greater  than  the  arc  bd. 
\  The  phaenomena  of  the  diflferent  seasons  of  the  year  will  appear 
plainly  from  the  following  observations.  Let  abcd  {Plate  III. 
Fig.  1.)  represent  the  plane  of  the  earth's  annual  orbit,  having'the 


*  It  is  demonstrated  by  all  writers  on  conic  sections,  that  a  line  drawn  from  one 
end  of  the  conjugate  axis  of  an  ellipsis  to  the  focus,  is  equal  to  half  the  transverse 
axis,  viz.  se=cb  or  ca. 

t  This  law  was  discovered  by  Kepler,  and  demonstrated  by  Sir  Isaac  Newton. 
See  the  Principia,  Book  III.  Prop.  xiii. 

t  Newton's  Principia,  Book  III.  Prop.  ii. 


Chap,  IV,  MOTION  OF  THE  EARTH.  83 

sun  in  the  focus  r ;  and  let  a  b,  an  imaginary  line  passing  through 
the  centre  of  the  earth,  be  perpendicular  to  this  plane ;  and  let 
the  axis  ns  of  the  earth  make  an  angle  of  23°  28'  with  this  perpen- 
dicular ;  then  if  the  earth  move  in  the  direction  a,  b,  c,  d,  in  such 
a  manner  that  ns  may  always  remain  parallel  to  itself,  and  pre- 
serve the  same  angle  with  a  b,  it  will  point  out  the  seasons  of  the 
year ;  for,  suppose  a  line  to  be  drawn  from  the  centre  of  the  sun 
to  the  centre  of  the  earth,  it  is  evident  that  the  sun  will  be  verti- 
cal to  that  part  of  the  earth  which  is  cut  by  this  line.  Now, 
when  the  earth  is  in  Libra  the  sun  will  appear  to  be  in  Aries  T, 
the  days  and  nights  will  be  equal  in  both  hemispheres,  and  the 
season  a  medium  between  summer  and  winter ;  the  line  dividing 
the  dark  and  light  hemispheres  passes  through  the  two  poles  n  and 
s,  and  consequently  divides  all  the  parallels  of  latitude,  as  pr, 
into  two  equal  parts ;  hence,  the  inhabitants  of  the  whole  face  of 
the  earth  have  their  days  and  nights  equal,  viz.  twelve  hours  each. 
While  the  earth  moves  from  Libra  .-^  to  Capricorn  V3,  the  north 
pole  N  will  become  more  and  more  enlightened,  and  the  south 
pole  s  will  be  gradually  involved  in  darkness,  consequently  the 
days  in  the  northern  hemisphere  will  continue  to  increase  in  length, 
and  in  the  southern  hemisphere  they  will  decrease  in  the  same 
proportion,  all  the  parallels  of  latitude  being  unequally  divided. 
When  the  earth  has  arrived  at  Capricorn  V3,  the  sun  will  appear 
to  be  in  Cancer  %  it  will  be  summer  to  the  inhabitants  of  the 
northern  hemisphere,  and  winter  to  those  in  the  southern ;  the 
inhabitants  at  the  north  pole,  and  wnthin  the  arctic  circle,  will 
have  constant  day,  and  those  at  the  south  pole,  and  within  the 
antarctic  circle,  will  have  constant  night.  While  the  earth  moves 
from  Capricorn  V3  to  Aries  T,  the  south  pole  will  become  more 
and  more  enlightened  ;  consequently  the  days  in  the  southern 
hemisphere  will  increase  in  length,  and  in  the  northern  hemisphere 
they  will  decrease.  When  the  earth  has  arrived  at  Aries  T,  the 
sun  will  appear  to  be  in  Libra  =i^,  and  the  days  and  nights  will 
again  be  equal  all  over  the  surface  of  the  earth.  Again,  as  the 
earth  moves  from  Aries  T  towards  Cancer  the  light  will  grad- 
ually leave  the  north  pole,  and  proceed  to  the  south ;  when  the 
earth  has  arrived  at  Cancer  it  will  be  summer  to  the  inhabi- 
tants in  the  southern  hemisphere,  and  winter  to  those  in  the 
northern ;  the  inhabitants  of  the  south  pole  (if  any)  will  have  con- 
tinual day,  those  at  the  north  pole  constant  night.  Lastly,  while 
the  earth  moves  from  Cancer  S  to  Capricorn  V3,  the  sun  will  ap- 
pear to  move  from  Capricorn  V3  to  Cancer  %  and  the  days  in  the 
northern  hemisphere  will  be  increasing,  while  those  in  the  south- 
.ern  will  be  diminishing  in  length ;  and  while  the  earth  moves  from 


84 


ORIGIN  OF  SPRINGS  AND  RIVERS. 


Part  L 


Capricorn  V3  to  Cancer  %  the  sun  will  appear  to  move  from  Can- 
cer S  to  Capricorn  V5,  the  days  in  the  northern  hemisphere  will 
then  be  decreasing,  and  those  in  the  southern  hemisphere  in- 
creasing. In  all  situations  of  the  earth,  the  equator  will  be  divid- 
ed into  two  equal  parts,  consequently  the  days  and  nights  at  the 
equator  are  always  equal.  Thus  the  different  seasons  are  clearly 
accounted  for,  by  the  incHnation  of  the  axis  of  the  earth  to  the 
plane  of  its  orbit,*  combined  with  the  parallel  motion  of  that  axis. 


CHAPTER  V. 

Of  the  Origin  of  Springs  and  Rivers,  and  of  theSaltness  of  the  Sea, 

Various  opinions  have  been  held  by  ancients  as  well  as  mod- 
ern philosophers,  respecting  the  origin  of  springs  and  rivers  ;  but 
the  true  cause  is  now  pretty  well  ascertained.  It  is  well  known 
that  the  heat  of  the  sun  draws  vast  quantities  of  vapour  from  the 
sea,  which,  being  carried  by  the  wind  to  all  parts  of  the  globe, 
and  being  converted  by  the  cold  into  rain  and  dew,  falls  down 
upon  the  earth ;  part  of  it  runs  down  into  the  lower  places,  form- 
ing rivulets ;  part  serves  for  the  purposes  of  vegetation,  and  the 
rest  descends  into  hollow  caverns  within  the  earth,  which  break- 
ing out  by  the  sides  of  the  hills  forms  little  springs  ;  many  of  these 


*  In  addition  to  these  observations,  the  author  farther  illustrates  the  seasons  of 
the  year  by  an  orrery;  and  sometimes  by  a  brass  wire  supported  on  two  stands  of 
different  heights,  corresponding  to  the  diameter  of  the  wire  circle,  and  the  obliquity 
of  the  ecliptic,  as  in  Ferguson's  Astronomy,  chap.  x.  But  as  this  last  method  does 
not  so  clearly  show  the  obliquity  of  the  axis  of  the  earth  to  the  plane  of  its  orbit, 
take  a  board  of  any  convenient  dimensions,  suppose  two  feet  across,  on  which 
describe  a  circle,  or  an  ellipsis  differing  little  from  a  circle,  draw  a  diameter  ofo, 
{Plate  III.  Fig.  \.)  and  parallel  to  this  diameter  let  several  lines  e/be  drawn,  then 
bore  several  holes  perpendicularly  down  in  the  points  e  e,  S^c.  of  the  circumference 
of  the  circle  ;  take  two  pieces  of  wire  crossing  each  other  in  an  agle  of  23°  28';  as 
a  g  and  nf,  of  which  a  g  the  perpendicular  wire  is  the  longer,  and  connect  them  by 
a  straight  wire  ef;  then  placing  a  small  globe  on  the  point  w,  and  a  light  in  the 
centre  of  the  circle  of  the  same  height  as  the  centre  of  the  httle  globe ;  let  the 
point  g  in  the  longer  wire  be  fixed  successively  in  the  holes  c  e,  &c.  in  the  circum- 
ference of  the  circle,  so  that  the  base  e,/,  of  the  wire  may  rest  on  the  lines  e^in 
the  plane  of  the  earth's  orbit,  the  seasons  of  the  year  will  be  agreeably  and  accu- 
rately illustrated.  If  the  Uttle  globe  be  placed  upon  the  point  a,  instead  of  the  point 
71,  and  the  same  method  be  observed  in  moving  the  wires  round  the  orbit,  there 
will  be  no  diversity  of  seasons.  The  diurnal  revolution  of  the  earth  maybe  shown 
by  moving  the  globe  round  the  wire  n  /,  as  an  axis,  with  the  finger. 


Chap,  V. 


OF  THE  SALTNESS  OF  THE  SEA. 


85 


springs  running  into  the  valleys  increase  the  brooks  or  rivulets, 
and  several  of  these  meeting  together  naake  a  river. 

Dr.  Halley*  says,  the  vapours  that  are  raised  copiously  from 
the  sea,  and  carried  by  the  winds  to  the  ridges  of  mountains,  are 
conveyed  to  their  tops  by  the  current  of  air ;  where  the  water 
being  presently  precipitated,  enters  the  crannies  of  the  moun- 
tains, down  which  it  ghdes  into  the  caverns,  till  it  meets  with  a 
stratum  of  earth  or  stone,  of  a  nature  sufficiently  solid  to  sustain 
it.  When  this  reservoir  is  filled,  the  superfluous  water,  following 
the  direction  of  the  stratum,  runs  over  at  the  lowest  place,  and 
in  its  passage  meets  perhaps  with  other  little  streams,  which  have 
a  similar  origin ;  these  gradually  descend  till  they  meet  with  an 
aperture  at  the  side,  or  foot  of  the  mountain,  through  which  they 
escape,  and  form  a  spring,  or  the  source  of  a  brook  or  rivulet. 
Several  brooks  or  rivulets,  uniting  their  streams,  form  small  riv- 
ers ;  and  these  again  being  joined  by  other  small  rivers,  and 
united  in  one  common  channel,  form  such  streams  as  the  Rhine, 
Rhone,  Danube,  &c. 

Several  springs  yield  always  the  same  quantity  of  wfiter  equally 
when  the  least  rain  or  vapour  is  afforded,  as  when  rain  falls  in 
the  greatest  quantities ;  and  as  the  fall  of  rain,  snow,  &c.  is  incon- 
stant or  variable,  we  have  here  a  constant  effect  produced  from 
an  inconstant  cause,  which  is  an  unphilosophical  conclusion. 
Some  naturalists,  therefore,  have  recourse  to  the  sea,  and  derive 
the  origin  of  several  springs  immediately  from  thence,  by  sup- 
posing a  subterraneous  circulation  of  percolated  waters  from  the 
fountains  of  the  deep. 

That  the  sun  exhales  as  much  vapour  as  is  sufficient  for  rain, 
is  past  dispute,  having  been  several  times  proved  by  actual  exper- 
iments. Dr.  Halleyf  determined  by  experiment  and  calcula- 
tionj,  that  in  a  summer's  day,  there  may  be  raised  in  vapours 
from  the  Mediterranean  5280  millons  of  tons  of  water,  and  yet 
the  Mediterranean  does  not  receive  from  all  its  rivers  above  1827 
millions  of  tons  in  a  day,  which  is  little  more  than  a  third  part 
of  what  is  exhausted  by  vapours§ ;  and  from  the  river  Thames, 


*  Philosophical  Transactions,  No.  192. 

t  Dr.  Halley  was  an  eminent  mathematician,  astronomer,  and  philosopher,  born 
in  London  in  the  year  1656. 

J  Philosophical  Transactions,  No.  212. 

§  As  evaporation  cannot  carry  off  fixed  salts,  it  would  appear  that  if  the  above 
calculation  be  accurate,  the  Mediterranean  would  be  more  salt  than  the  ocean,  but 
it  must  be  remembered  that  a  current  sets  constantly  out  of  the  Atlantic  Ocean 
into  the  Mediterranean. 


86  ORIGIN  OF  SPRINGS  AND  RIVERS,  AND  Part  I. 

twenty  millions  three  hundred  thousand  tons  may  be  raised  in 
one  day  in  a  similar  manner. — In  the  Old  Continent,  there  are 
about  430  rivers  which  fall  directly  into  the  ocean,  or  into  the 
Mediterranean  and  Black  Seas,  and  in  the  New  Continent,  scarcely 
180  rivers  are  known,  which  fall  directly  into  the  sea  ;  but  in  this 
number,  only  the  greater  rivers  are  comprehended.*  All  these 
rivers  carry  to  the  sea  a  great  quantity  of  mineral  and  saline  par- 
ticles, which  they  wash  from  the  different  soils  through  which 
they  pass,  and  the  particles  of  salt,  which  are  easily  dissolved,  are 
conveyed  to  the  sea  by  the  water.  Dr.  Halley  imagines  that  the 
saltness  of  the  sea  proceeds  from  the  salts  of  the  earth  only,  which 
rivers  convey  thither,  and  that  it  was  originally  fresh.  So  that 
its  saltness  will  continue  to  increase ;  for,  the  vapours  which  are 
exhaled  from  the  sea  are  entirely  fresh,  or  devoid  of  saline  par- 
ticles. Others  imagine  that  there  is  a  great  number  of  rocks  of 
salt  at  the  bottom  of  the  sea,  and  from  these  rocks  it  acquires  its 
saltness.  Some  writers,  again,  have  imagined  that  the  sea  was 
created  salt  that  it  might  not  corrupt ;  but  it  may  well  be  supposed 
that  the  sea  is  preserved  from  corruption  by  the  agitations  of  the 
wind,  and  from  the  flux  and  reflux  of  the  tide,  as  much  as  by  the 
salt  it  contains,  for,  when  sea-water  is  kept  in  a  barrel,  it  corrupts 
in  a  few  days.  The  Honourable  Mr.  Boylef  relates  that  a  mar- 
iner, becalmed  for  thirteen  days,  found  at  the  end  of  that  time, 
the  sea  so  infected,  that  if  the  calm  had  continued,  the  greatest  ^ 
part  of  his  people  on  board  would  have  perished. — The  sea  is 
nearly  equally  salt  throughout,  under  the  equinoctial  line  and  at 
the  Cape  of  Good  Hope,  though  there  are  some  places  on  the 
Mozambique  coast  where  it  is  Salter  than  elsewhere.  It  is  also 
asserted  that  it  is  not  quite  so  salt  under  the  arctic  circle  as  in 
some  other  latitudesj  ;  this  probably  may  proceed  from  the  great 
quantity  of  snow,  and  the  great  rivers  which  fall  into  those  seas : 
to  which  we  may  add,  that  the  sun  does  not  draw  such  quantities 
of  fresh  water,  or  vapours,  from  those  seas  as  in  hot  countries. 

It  is  worthy  of  remark  that  all  lakes  from  which  rivers  derive 
their  origin,  or  which  fall  into  the  course  of  rivers,  are  not  saline  ;§ 


*  Buffon's  Natural  History. 

t  A  younger  son  of  the  Earl  of  Cork,  and  one  of  the  most  celebrated  philoso- 
phers in  Europe,  born  at  Lismore,  in  the  county  of  Waterford,  1626-7.  See  his 
treatise  on  the  Saltness  of  the  Sea,  published  in  1674. 

I  In  a  System  of  Chemistry,  by  Dr.  Thompson,  of  Edinburgh,  Vol.  \v.  fourth  edition^ 
page  141,  it  is  stated,  that  the  ocean  contains  most  salt  between  10°  and  20°  south 
latitude,  and  that  the  proportion  of  salt  is  the  least  in  latitude  57"  north. 

§  Buffon's  Natural  History,  Chap.  II. 


Chap,  V.  OP  THE  SALTNESS  OF  THE  SEA.  87 

and  almost  all  those,  on  the  contrary,  which  receive  rivers,  with- 
out other  rivers  issuing  from  them,  are  saline :  this  seems  to  fa- 
vour Dr.  Halley's  opinion  respecting  the  saltness  of  the  sea ;  for 
evaporation  cannot  carry  off  fixed  salts,  and  consequently  those 
salts  which  rivers  carry  into  the  sea  remain  there.  It  is  asserted* 
to  be  the  peculiar  property  of  sea-water,  that  when  it  is  abso- 
lutely salt,  it  never  freezes ;  and  that  the  islands  or  rocks  of  ice 
which  float  in  the  sea  near  the  poles,  are  originally  frozen  in  the 
rivers,  and  carried  thence  to  the  sea  by  the  tide  ;  where  they  con- 
tinue to  accumulate  by  the  great  quantities  of  snow  and  sleet 
which  fall  in  those  seas.  According  to  this  opinion,  great  quan- 
tities of  ice  can  be  produced  only  from  great  quantities  of 
fresh  water,  or  from  large  rivers ;  and  as  large  rivers  can  only 
flow  from  large  tracts  of  land,  it  would  appear  that  there  must 
be  immense  tracts  of  land  near  the  south  pole,  for  the  Antarctic 
Ocean  abounds  with  fields  or  mountains  of  ice,  as  well  as  the 
Arctic  Ocean  ;  but  our  circumnavigators  have  traversed  the 
Southern  Ocean  to  upwards  of  seventy  degrees  south  latitude, 
without  discovering  any  land.f  With  respect  to  the  freezing  of 
salt  water,  we  have  several  instances  of  the  Baltic  J  and  other 
seas  being  frozen  over,  when  the  ice  on  the  surface  could  never 
proceed  from  rivers.  It  is  true  that  the  sailors  frequently  take 
large  pieces  of  the  rocks  of  ice,  and  thaw  them  for  the  use  of  the 
ship's  company,  and  always  find  the  water  fresh  ;  but  it  does  not 
follow  from  this  that  the  ice  is  formed  in  the  rivers.  As  fresh 
water  only  is  extracted  from  sea-water  by  the  heat  of  the  sun, 
and  carried  into  the  atmosphere,  may  not  the  fresh,  without  the 
saline  particles  of  sea-water,  be  converted  into  ice  by  extreme 
cold? 


*  Emerson's  Geography,  page  64. 

t  Mr.  William  Smith,  master  of  the  brig  WiUiams,  of  BIythe,  Northumberland, 
in  a  voyage  from  Buenos  Ayres  to  Valparaiso,  in  Chili,  in  order  more  easily  to 
weather  Cape  Horn,  steered  an  unusual  southerly  course,  and  on  the  19th  of  Feb- 
ruary 1819,  lat.  62°  \T  S.  long.  60°  12'  W.  discovered  land  :  he  afterwards  ascer- 
tained the  existence  of  the  coast  for  the  distance  of  250  miles.  An  account.of  this 
discovery,  with  plates  of  the  appearance  of  the  land,  &c.  may  be  seen  in  the  Edin- 
burgh Philosophical  Journal,  Vol.  III.  October  1820,  page  367.  This  newly-dis- 
covered land  is  called  JVcio  South  Shetland. 

X  The  Baltic  Sea  is  not  so  salt  as  the  ocean,  and  the  proportion  of  salt  is  in- 
creased by  a  west  wind,  and  still  more  by  a  north-west  wind :  a  proof  that  not 
only  the  saltness  of  the  Baltic  is  derived  from  the  ocean,  but  that  storms  have  a 
much  greater  effect  upon  the  waters  of  the  ocean  than  has  been  supposed.  Dr. 
Thompson's  Chemistry,  vol.  iv.  page  141.— The  Baltic  Sea  has  little  or  no  tides,  and 
a  current  runs  constantly  through  the  Sound  into  the  Cattegate  Sea. 


88 


OF  THE  FLUX  AND 


Part  I. 


CHAPTER  VI. 

Of  the  Flux  and  Reflux  of  the  Tides. 

A  TIDE  is  that  motion  of  the  water  in  the  seas  and  rivers,  by 
which  they  are  found  to  rise  and  fall  in  a  regular  succession  ;  and 
this  flowing  and  ebbing  is  caused  by  the  attraction  of  the  sun  and 
moon.* 

Suppose  the  earth  to  be  entirely  covered  by  a  fluid  as  a,  b,  z, 
c,  D,  Q,  N.  {Plate  III.  Figure  2.)  and  the  action  of  the  sun  and 
moon  to  have  no  eflfect  upon  it,  then  it  is  evident  that  all  the  par- 
ticles, being  equally  attracted  towards  the  centre  o  of  the  earth, 
would  form  an  exact  spherical  surface  ;  except,  that  by  the  revo- 
lution of  the  earth  on  its  axis  s',  the  attraction  from  b  towards  o, 
and  from  q  towards  o  would  be  a  little  diminished  by  the  centrif- 
ugal force.  Let  the  moon  at  m  now  exert  her  influence  upon  the 
water ;  then  because  the  power  of  attraction  diminishes  as  the 
square  of  the  distance  increases,  those  parts  will  be  the  most  at- 
tracted which  are  nearest  to  the  moon,  and  their  tendency  towards 
o  will  be  diminished :  the  waters  at  z,  b,  and  c,  will  therefore 
rise,  and  at  z,  which  is  nearest  to  the  moon,  they  will  be  the 
highest ;  but  when  the  waters  in  the  zenith  z  are  elevated,  those  in 
the  nadir  n  are  likewise  elevated  in  a  similar  manner;  this  is  known 
from  experience,  for  we  have  high  water  when  the  moon  is  in  our 
nadir  as  w^ell  as  when  she  is  in  our  zenith  ;  we  therefore  conclude 
that,  when  the  moon  is  in  our  zenith,  our  antipodes  have  high 
water :  the  truth  of  this,  as  well  as  every  other  phenomenon  res- 
pecting the  tides,  will  be  discussed  in  the  following  theorems. 

Theorem  I.f  The  parts  of  the  earth  directly  under  the  moon,  or 
where  the  moon  is  in  the  Zenith  as  at  z;  (Plate  III.  Figure  3.)  and 
those  places  which  are  diametrically  opposite  to  the  former,  or  un- 
der the  Nadir  as  at  n,  will  have  high  water  at  the  same  time : 

Because  the  power  of  gravity  decreases  as  the  square  of  the 
distance  increases ;  the  waters  at  a,  b,  z,  c,  d,  on  the  side  of  the 
earth  next  the  moon  m,  will  be  more  attracted  by  the  moon  than 
the  central  parts  o  of  the  earth,  and  the  central  parts  will  be 


*  This  was  known  to  the  ancients :  Pliny  expressly  says  that  the  cause  of  the  ebb 
and  flow  is  in  the  sun,  which  attracts  the  waters  of  the  ocean,  and  that  they  also 
rise  in  proportion  to  the  proximity  of  the  moon  to  the  earth.  Dr.  Huttori's  Math. 
Dictionary,  word  Tides. 

t  A  theorem  is  a  proposition  which  admits  of  proof,  or  demonstration,  from  de- 
finitions clearly  understood,  and  from  the  known  general  properties  of  the  subject 
under  consideration. 


Chap.  VI. 


REFLUX   OF  THE  TIDES. 


89 


more  attracted  than  the  surface  n  on  the  opposite  side  of  the 
earth ;  therefore  the  distance  between  the  centre  of  the  earth 
and  the  surface  of  the  water,  under  the  zenith  and  nadir,  will  he 
increased.  For,  let  three  bodies,  z,  o,  and  n,  be  equally  attracted 
by  M ;  then  it  is  evident  they  will  all  move  equally  fast  towards 
M,  and  their  mutual  distances  from  each  other  will  continue  the 
same  ;  but  if  the  bodies  be  unequally  attracted  by  m,  that  body 
which  is  the  most  attracted  will  move  the  fastest,  and  its  aistance 
from  the  other  bodies  will  be  increased.  Now,  by  the  law  of 
gravitation,  m  will  attract  z  more  strongly  than  it  does  o,  by 
which  the  distance  between  z  and  o  will  be  increased.  In  like 
manner  o  being  more  strongly  attracted  than  n,  the  distance  be- 
tween o  and  N  will  be  increased ;  suppose  now  a  number  of  bod- 
ies, A,  B,  z,  c,  D,  F,  N,  E,  placcd  rouud  o,  to  be  attracted  by  m,  the 
parts  z  and  n  will  have  their  distances  from  o  increased  ;  while 
the  parts  a  and  d,  being  nearly  at  the  same  distance  from  m  as  o 
is,  will  not  recede  from  each  other,  but  will  rather  approach  near 
to  o  by  the  oblique  attraction  of  m.  Hence  if  the  whole  earth 
were  composed  of  bodies  similar  to  a,  b,  z,  c,  d,  f,  n,  e,  and  to 
be  similarly  attracted  by  m,  the  section  of  the  earth,  formed  by  a 
plane  passing  through  the  moon  and  the  earth's  centre,  would  be 
a  figure  resembling  an  ellipsis,  having  its  longer  axis  zn  directed 
towards  the  moon ;  and  its  shorter  axis  ad  in  the  horizon.  The 
figure  of  the  earth  therefore  would  be  an  oblong  spheroid  having 
its  longer  axis  directed  to  the  moon,  consequently  it  will  be  high 
water  in  the  zenith  and  nadir  at  the  same  time  ;  and  as  the  earth 
turns  round  its  axis  from  the  moon  to  the  moon  again  in  about 
24  hours  and  48  minutes,  there  will  be  two  tides  of  flood  and  two 
of  ebb  in  that  time,  agreeably  to  experience. 

According  to  the  foregoing  explanation  of  the  ebbing  and 
flowing  of  the  sea,  every  part  of  the  earth  is  gravitating  towards 
the  moon  ;  but  as  the  earth  revolves  round  the  sun,  every  part  of 
it  gravitates  towards  the  sun  likewise  ;  it  may  be  asked  how  is 
this  possible  at  the  time  of  full  moon,  when  the  moon  is  at  m  and 
the  sun  at  s  ;  has  the  earth  a  tendency  to  fall  contrary  ways  at 
the  same  time  ?  This  is  a  very  natural  question,  but  it  must  be 
considered  that  it  is  not  the  centre  of  the  earth  that  describes  the 
annual  orbit  round  the  sun,  but  the  common  centre  of  gravity  of 
the  earth  and  moon  together ;  and  that  whilst  the  earth  is 
moving  round  the  sun,  it  also  describes  a  circle  round  that  centre 
of  gravity,  about  which  it  revolves  as  many  times  as  the  moon 
revolves  round  the  earth  in  a  year.*    The  earth  is  therefore  con- 


*  Ferguson's  Astronomy,  Article  298. 

13 


90 


OF  THE  FLUX  AND 


Part  I. 


stantly  falling  towards  the  moon,  from  a  tangent  to  the  drcle  which 
it  describes  round  the  common  centre  of  gravity  of  the  earth  and 
moon.  Let  m  represent  the  moon,  {Plate  III.  Figure  4.,)  tw  a 
part  of  the  moon's  orbit,  and  as  the  earth  is  supposed  to  contain 
about  forty  times  the  quantity  of  matter  which  is  contained  in  the 
moon,  the  common  centre  of  gravity  from  the  centre  of  the  earth 
towards  the  moon  will  be  considerably  less  than  the  earth's  diam- 
eter.* Let  this  common  centre  of  gravity  be  represented  by  c. 
Then  whilst  the  moon  goes  round  her  orbit,  the  centre  of  the 
earth  describes  the  circle  doe  round  c,  to  which  circle  o  «  is  a 
tangent :  therefore  when  the  moon  has  gone  from  m  to  a  little 
past  w,  the  earth  has  moved  from  o  to  e ;  and  in  that  time  has 
fallen  towards  the  moon  from  the  tangent  at  a  to  e.  This  figure 
is  drawn  for  the  new  moon,  but  the  earth  will  tend  towards  the 
moon  in  the  same  manner  during  its  whole  revolution  round  c. 

Theorem  IL  Those  parts  of  the  earth  where  the  moon  appears  in 
the  horizon,  or  90  degrees  distant  f  rom  the  Zenith  and  Nadir, 
as  at  A  and  d  (Plate  IIL  Figure  3.)  will  have  ebb  or  low  water : 

For,  as  the  waters  under  the  zenith  and  nadir  rise  at  the  same 
time,  the  waters  in  their  neighbourhood  will  press  towards  those 
places  to  maintain  the  equilibrium  ;  and  to  supply  the  place  of 
these  waters,  others  will  move  the  same  way,  and  so  on  to  places 
of  90  degrees  distance  from  the  zenith  and  nadir;  consequently  at 
A  and  r>  where  the  moon  appears  in  the  horizon,  the  waters  will 
have  more  liberty  to  descend  towards  the  centre  of  the  earth ; 


*  The  common  centre  of  gravity  of  two  bodies  is  found  thus  :  as  the  sum  of  the 
weights,  or  quantities  of  matter  in  the  two  bodies  is  to  their  distance  from  each 
other,  so  is  the  weight  of  the  less  body  to  the  distance  of  the  greater  from  the 
centre  of  gravity.  Now  if  the  quantity  of  matter  in  the  moon  be  represented  by 
1,  that  in  the  earth  by  (40),  and  the  distance  of  the  earth  from  the  moon  be  esti- 
mated at  240,000  miles,  then  (40 -j-  1) :  240,000  : :  1  ;  (5853)  jniles,  the  distance  of 
the  centre  of  the  earth  from  the  common  centre  of  gravity,  Mr.  A.  Walker,  in 
the  11th  lecture  of  his  Familiar  Philosophy,  ingeniously  accounts  for  its  being  high 
water  in  the  zenith  and  nadir  at  the  same  time,  in  the  following  manner.  "  The 
parts  of  the  earth  that  are  farthest  from  the  moon,  will  have  a  swifter  motion  round 
the  centre  of  gravity  than  the  other  parts ;  thus  the  side  n  will  describe  the  circle 
n  V  T,  while  the  side  m  will  only  describe  the  small  circle  m  r  s,  round  the  centre  of 
gravity  c.  Now,  as  every  thing  in  motion  always  endeavours  to  go  forward  in  a 
straight  line,  the  water  at  n  having  a  tendency  to  go  off  in  the  line  n  q,  will  in  a 
degree  overcome  the  power  of  gravity,  and  swell  into  a  heap  or  protuberance,  as 
represented  in  the  figure,  and  occasion  a  tide  opposite  to  that  caused  by  the  attrac- 
tion of  the  moon." 


Chap,  VI. 


IIEFLUX  OF  THE  TIDES. 


91 


and  therefore  in  those  places  they  will  be  the  lowest.  Hence  it 
plainly  appears,  that  the  ocean,  if  it  covered  the  whole  surface  of 
the  earth,  would  be  a  spheroid,  (as  was  observed  in  the  foregoing 
theorem,)  the  longer  diameter,  as  zn,  passing  through  the  place 
where  the  moon  is  vertical,  and  the  shorter  diameter,  as  ad,  pass- 
ing through  the  rational  horizon  of  that  place.  And  as  the  moon 
apparently*  shifts  her  position  from  east  to  west  in  going  round 
the  earth  every  day,  the  longer  diameter  of  the  spheroid  follow- 
ing her  motion  will  occasion  the  two  floods  and  ebbs  in  about  24 
hours  and  48  mimitesf ,  the  time  w4iich  any  meridian  of  the  earth 
takes  in  revolving  from  the  moon  to  the  moon  again ;  or  the  time 
elapsed  (at  a  medium)  between  the  passage  of  the  moon  over 
the  meridian  of  any  place,  to  her  return  to  the  same  meridian. 

The  meridian  altitude  of  the  moon  at  any  place  is  her  greatest 
height  above  the  horizon  at  that  place,  hence  the  greater  the 
moon's  meridian  altitude  is,  the  greater  the  tides  will  be ;  for 
they  increase  from  the  horizon  d  to  the  point  z  under  the  zenith, 
and  the  greater  the  moon's  meridian  depression  is  below  the  hori- 
zon, the  greater  the  tides  will  be ;  for  they  increase  from  the 
horizon  d  towards  n  the  point  below  the  nadir,  and  consequently 
as  the  tides  increase  from  d  to  n,  the  tides  in  their  antipodes  will 
increase  from  a  to  z. 

Theorem  III.  The  time  of  high  water  is  not  precisely  at  the  time 
of  the  moon^s  coming  to  the  meridian,  hut  about  an  hour  after : 

For,  the  moon  acts  with  some  force  after  she  has  passed  the 
meridian,  and  by  that  means  adds  to  the  libratory  or  waving  mo- 
tion, which  the  waters  had  acquired  whilst  she  was  on  the  me- 
ridian. 


*  The  real  motion  of  the  moon  is  from  the  west  towards  the  east ;  for  if  she  be 
seen  near  any  fixed  star  on  any  night,  she  will  be  seen  about  13  degrees  to  the 
eastward  of  that  star  the  next  night,  and  so  on.  The  moon  goes  round  her  or- 
bit from  any  fixed  star  to  the  same  again  in  about  27  days  and  8  hours.  Hence 
27  d.  8  h.  :  360<^  :  :  1  d. :  IS**  10'  4:1". Q,  the  mean  motion  of  the  moon  in  24  hours. 

t  The  mean  motion  of  the  moon  in  24  hours  is  13^  W  14".6,  and  the  mean  ap- 
parent motion  of  the  sun  in  the  same  time  is  59'  8''.2,  {see  the  note  to  definition  61. 
page  14.)  the  moon's  motion  is  therefore  12  \  V  swifter  than  the  apparent  mo- 
tion of  the  sun  in  one  day,  which,  reckoning  4  minutes  to  a  degree,  amounts  to  48 
minutes  44  seconds  of  time. 


92 


OF  THE  FLTJX  AND 


Part  I. 


Theorem  IV.  The  tides  are  greater  than  ordinary  twice  every 
month ;  viz.  at  the  time  of  new  and  full  moon,  and  these  are 
ca/W  Spring-tides:    (Plate  III.  Figure  III.) 

For  at  these  times  the  actions  of  both  the  sun  and  moon  con- 
cur to  draw  in  the  same  straight  line  smzon,  and  therefore  the 
sea  must  be  more  elevated.  In  conjunction,  or  at  the  new  moon, 
when  the  sun  is  at  s  and  the  moon  at  m  both  on  the  same  side  of 
the  earth,  their  joint  forces  conspire  to  raise  the  water  in  the  ze- 
nith at  z,  and  consequently  (according  to  Theorem  I.)  at  n  the 
nadir  likewise.*  When  the  sun  and  moon  are  in  opposition,  or 
at  the  full  moon  when  the  sun  is  at  s  and  the  moon  at  m,  the  earth 
being  between  them  ;  while  the  sun  raises  the  water  at  z  under 
the  zenith  and  at  n  under  the  nadir,  the  moon  raises  the  water  at 
N  under  the  nadir  and  at  z  under  the  zenith. 


+  Mr.  Walker  says  (Lecture  11th),  that  at  new  moon  "The  sun's  influence  is 
added  to  that  of  the  moon,  and  the  centre  of  gravity  c  (Plate  III.  Figure  4.)  will, 
therefore,  be  removed  farther  from  the  earth  than  mc,  and  of  course,  increase  the 
centrifugal  tendency  of  the  tide  n  :  hence  both  the  attracted  and  centrifugal  tides 
are  spring-tides  at  that  time. — "  But  spring-tides  take  place  at  the  full  as  well  as 
at  the  change  of  the  moon.  Now  it  has  been  premised,  that  if  we  had  no  moon, 
the  sun  would  agitate  the  ocean  in  a  small  degree  and  make  two  tides  every  twen- 
ty-four hours,  though  upon  a  small  scale.  The  moon's  centrifugal  tide  at  z  (Plate 
III.  Figure  3.)  being  increased  by  the  sun's  attraction  at  s,  will  make  the  protuber- 
ance a  spring-tide;  and  the  sun^s  centrifugal  tide  at  n  will  be  reinforced  by  the 
moon's  attraction  at  m,  and  make  the  protuberance  n  a  spring-tide  ;  so  spring- 
tides take  place  at  the  full  as  well  as  at  the  change  of  the  moon." — Suppose  the 
moon  to  be  taken  away  (Plate  III.  Figure  4.)  the  common  centre  of  gravity  of  the 
earth  and  the  sun  would  fall  entirely  within  the  body  of  the  sun,  round  which  the 
earth  revolves  in  a  year,  at  the  rate  of  about  a  degree  in  a  day  ;  hence  the  parts  n 
of  the  earth  farthest  from  the  sun  would  have  a  httle  more  tendency  to  recede  from 
the  centre  of  motion  s,  than  the  parts  m  which  are  the  nearest.  So  that  if  the  sun 
were  on  the  meridian  of  any  place  it  would  be  high  water  at  that  place  by  the  sun's 
attraction,  and  it  would  at  the  same  time  be  high  water  at  the  antipodes  of  that 
place  by  the  centrifugal  tendency  of  n  ;  consequently  as  the  earth  revolves  on  its 
axis  from  noon  to  noon  in  24  hours,  there  would  be  tv.'o  tides  of  flood  and  two  of 
ebb  during  that  time.  If  the  line  m  c  be  increased  when  the  moon  is  in  conjunc- 
tion with  the  sun,  so  as  to  cause  the  point  n  to  describe  a  larger  circle  than  ri  v  y, 
and  also  the  point  m  to  describe  a  larger  circle  than  mr  s  round  the  centre  of  grav- 
ity c  ;  when  the  sun  is  in  opposition  to  the  moon,  the  line  m  c  will  be  diminished, 
11  will  therefore  describe  a  smaller  circle  than  n  v  t,  and  ?n  will  describe  a  smaller 
circle  than  m  r  s.  Hence  it  appears  that  the  centrifugal  tendency  of  n  is  greater  at 
the  new  moon  than  it  is  at  the  full  moon,  and  m  is  likewise  more  strongly  attracted 
at  the  same  time  ;  the  spring-tides  at  the  time  of  conjunction  would  therefore  be 
considerably  greater  than  at  the  time  of  opposition,  were  not  the  moon's  centrif- 
ugal tide  at  this  time  attracted  by  the  sun,  and  the  sun's  centrifugal  tide  added  to 
to  that  caused  by  the  moon's  attraction. 


Chap.  VI. 


REFLUX  OF  THE  TIDES. 


93 


Theorem  V.  The  tides  are  less  than  ordinary  twice  every  month  ; 
that  is,  about  the  time  of  the  first  and  last  quarters  of  the  moon, 
and  these  are  called  Neap-tides  :  (Plate  III.  Figure  3.) 

Because  in  the  quadratures,  or  when  the  moon  is  90  degrees 
from  the  sun,  the  sun  acts  in  the  direction  sd  and  elevates  the 
water  at  d  and  a  ;  and  the  moon  acting  in  the  direction  mz  or  mN 
elevates  the  water  at  z  and  n  ;  so  that  the  sun  raises  the  water 
where  the  moon  depresses  it,  and  depresses  the  water  where  the 
moon  raises  it ;  consequently  the  tides  are  formed  only  by  the 
difference  between  the  attractive  force  of  the  sun  and  moon. — 
The  waters  at  z  and  n  will  be  more  elevated  than  the  waters  at 
D  and  A,  because  the  moon's  attractive  force  is  four*  times  that 
of  the  sun. 

Theorem  VI.  The  spring  tides  do  not  happen  exactly  on  the  day 
of  the  change  or  full  moon,  nor  the  neap-tides,  exactly  on  the 
days  of  the  quarters,  but  a  day  or  two  afterwards. 

When  the  attractions  of  the  sun  and  moon  have  conspired  to- 
gether for  a  considerable  time,  the  motion  impressed  on  the  wa- 
ters will  be  retained  for  some  time  after  their  attractive  forces 
cease,  and  consequently  the  tide  w^ill  continue  to  rise.  In  like 
manner  at  the  quarters,  the  tide  will  be  the  lowest  when  the 
moon's  attraction  has  been  lessened  by  the  sun's  for  several  days 
together. — If  the  action  of  the  sun  and  moon  were  suddenly  to 
cease,  the  tides  would  continue  their  course  for  some  time,  as  the 
waves  of  the  sea  continue  to  be  agitated  after  a  storm. 


*  Sir  Isaac  Newton,  Cor.  3  Prop.  XXXVII.  Book  III.  Princip.  makes  the  force 
of  the  moon  to  that  of  the  sun,  in  raising  the  waters  of  the  ocean,  as  4.4815  to  1  : 
and  in  Corol.  1.  of  the  same  proposition  he  calculates  the  height  of  the  solar  tide  to 
be  2  feet  0  inch  |,  the  lunar  tide  9  feet  1  inch  |,  and  by  their  joint  attraction  11  feet 
2  inches ;  when  the  moon  is  in  Perigee  the  joint  forces  of  the  sun  and  moon  will 
raise  the  tides  upwards  of  13^  feet. — Sir  Isaac  Newton's  measures  are  in  French 
feet  in  the  Principia.    I  have  turned  them  into  English  feet. 

Mr.  Emerson,  in  his  Fluxions,  Section  III.  Prob.  25.  calculates  the  greatest 
height  of  the  solar  tide  to  be  1.63  feet,  the  lunar  tide  7.28  feet,  and  by  their  joint 
attraction  8.91  feet,  making  the  force  of  the  sun  to  that  of  the  moon  as  1  to  4.4815. 

Dr.  Horsely,  the  late  bishop  of  St.  Asaph,  estimates  the  force  of  the  moon  to  that 
of  the  sun  as  5.0469  to  1.  See  his  edition  of  the  Principia,  lib.  3.  Sect.  3.  Prop. 
XXXVI.  and  XXXVII. 

Mr.  Walker,  in  Lect.  11th  of  his  Familiar  Philosophy,  states  the  influence  of  the 
sun  to  be  to  the  influence  of  the  moon  to  raise  the  water,  as  3  is  to  10,  and  their 
joint  force  13. 


94 


or  THE  PLtTX  AND 


Part  I. 


Theorem  VII.  When  the  moon  is  nearest  to  the  earth,  or  in  Peri- 
gee, the  tides  increase  more  than  in  similar  circumstances  at 
other  times : 

For  the  power  of  attraction  increases  as  the  square  of  the  dis- 
tance of  the  moon  from  the  earth  decreases ;  consequently  the 
moon  must  attract  most  when  she  is  nearest  to  the  earth. 

Theorem  VIII.  The  spring-tides  are  greater  a  short  time  before 
the  vernal  equinox,  and  after  the  autumnal  equinox,  viz.  about 
the  latter  end  of  March  and  September,  than  at  any  other  time 
of  the  year :  (Plate  III.  Figure  III.) 

Because  the  sun  and  moon  will  then  act  upon  the  equator  in 
the  direction  af  b,  consequently  the  spheroidal  figure  of  the  tides 
will  then  revolve  round  its  longer  axis,  and  describe  a  greater  cir- 
cle than  at  any  other  time  of  the  year ;  and  as  this  great  circle  is 
described  in  the  same  time  that  a  less  circle  is  described,  the  wa- 
ters will  be  thrown  more  forcibly  against  the  shores  in  the  for- 
mer circumstances  than  the  latter. 

Theorem  IX.  Lakes  are  not  subject  to  tides  ;  and  small  inland 
seas,  such  as  the  Mediterranean  and  Baltic,  are  little  subject  to 
tides.  In  very  high  latitudes  north  or  south  the  tides  are  also 
inconsiderable. 

The  lakes  are  so  small,  that  when  the  moon  is  vertical  she  at- 
tracts every  part  of  them  alike.  The  Mediterranean  and  Baltic 
seas  have  very  small  elevations,  because  the  inlets  by  which  they 
communicate  with  the  ocean  are  so  narrow,  that  they  cannot,  in 
so  short  a  time,  receive  or  discharge  enough  to  raise  or  lower 
their  surfaces  sensibly. 

Theorem  X.  The  time  of  the  tides  happening  in  particular  places, 
and  likewise  their  height,  may  be  very  different  according  to  the 
situation  of  these  places : 

For  the  motion  of  the  tides  is  propagated  swifter  in  the  open 
sea,  and  slower  through  narrow  channels  or  shallow  places ; 
and  being  retarded  by  such  impediments  the  tides  cannot  rise  so 
high. 

General  Observation. 


The  new  and  full  moon  spring-tides  rise  to  different  heights. 


Chap  VI. 


REFLUX  OF  THE  TIDES^ 


95 


The  morning  tides  differ  generally  in  their  rise  from  the  eve-' 
ning  tides. 

In  winter  the  morning  tides  are  highest. 

In  summer  the  evening  tides  are  highest. 

The  tides  follow  or  flow  towards  the  course  of  the  moon,  when 
they  meet  with  no  impediment.  Thus  the  tide  on  the  coast  of 
Norway  flows  to  the  south  (towards  the  course  of  the  moon)  ; 
from  the  North-cape  in  Norway  to  the  Naze  at  the  entrance  of 
the  Scaggerac,  or  Cattegate  Sea,  where  it  meets  with  the  cur- 
rent which  sets  constantly  out  of  the  Baltic  Sea,  and  consequently 
prevents  any  tide  rising  in  the  Scaggerac.  The  tide  proceeds  to 
the  southward,  along  the  east  coast  of  Great  Britain,  supplying 
the  ports  successively  with  high  water,  beginning  first  on  the 
coast  of  Scotland.  Thus  it  is  high  water  at  Tynemouth  Bar,  at 
the  time  of  new  and  full  moon,  about  three  hours  after  the  time 
of  high  water  at  Aberdeen  ;  it  is  high  water  at  Spurn-head  about 
two  hours  after  the  time  of  high  water  at  Tynemouth  Bar  ;  in  an 
hour  more  it  runs  down  the  Humber,  and  makes  high  water  at 
Kingston  upon  Hull ;  it  is  about  three  hours  running  from  Spurn- 
head  to  Yarmouth  Road  ;  one  hour  in  running  from  Yarmouth 
Road  to  Yarmouth  Pier  ;  2^  hours  running  from  Yarmouth  Road 
to  Harwich  ;  Ij  hour  in  passing  from  Harwich  to  the  Nore,  from 
whence  it  proceeds  up  the  Thames  to  Gravesend  and  London. 
From  the  Nore,  the  tide  continues  to  flow  southward  to  the  Downs 
and  Godwin  Sands,  between  the  north  and  south  Foreland  in 
Kent,  where  it  meets  the  tide  which  flows  out  of  the  English 
Channel,  through  the  Strait  of  Dover. 

While  the  tide,  or  high  water,  is  thus  gliding  to  the  southward, 
along  the  eastern  coast  of  Great  Britain,  it  also  sets  to  the  south- 
ward along  the  western  coasts  of  Scotland  and  Ireland  ;  but,  on 
account  of  the  obstructions  it  meets  with  by  the  Western  Islands 
of  Scotland,  and  the  narrow  passage  between  the  north-east  of 
Ireland  and  the  south-west  of  Scotland,  the  tide  in  the  Irish  Sea 
comes  round  by  the  south  of  Ireland  through  St.  George's  Chan- 
nel, and  runs  in  a  north-east  direction  till  it  meets  the  tide  be- 
tween Scotland  and  Ireland  at  the  north-west  part  of  the  Isle  of 
Man.  This  may  be  naturally  inferred  from  its  being  high  water 
at  Waterford  above  three  hours  before  it  is  high  water  at  Dub- 
lin, and  it  is  high  water  at  Dundalk  Bay  and  the  Isle  of  Man 
nearly  at  the  same  time.  That  the  tide  continues  its  course 
southward  may  be  inferred  from  its  being  high  water  at  Ushant, 
opposite  to  Brest  in  France,  about  an  hour  after  the  time  of  high 
water  at  Cape  Clear,  on  the  southern  coast  of  Ireland.  Between 
the  Lizard  Point  in  Cornwall  and  the  Island  of  Ushant,  the  tide 


96 


OF  THE  FLUX, 


Part  t 


flows  eastward,  or  east-north-east,  up  the  English  Channel,  along 
the  coasts  of  England  and  France,  and  so  on  through  the  Strait 
of  Dover,  till  it  comes  to  the  Godwin  Sands  or  Galloper,  where 
it  meets  the  tide  on  the  eastern  coast  of  England,  as  has  been  ob- 
served before.  The  meeting  of  these  two  tides  contributes 
greatly  towards  sending  a  powerful  tide  up  the  river  Thames  to 
London ;  and,  when  the  natural  course  of  these  two  tides  has 
been  interrupted  by  a  sudden  change  of  the  wi.id,  so  as  to  accel- 
erate the  tide  which  it  had  before  retarded,  and  to  drive  back  that 
tide  which  had  before  been  driven  forward  by  the  wind,  this  cause 
has  been  known  to  produce  twice  high  water  in  the  course  of 
three  or  four  hours.  The  above  account  of  the  British  tides 
seems  to  contradict  the  general  theory  of  the  motion  of  the  tides, 
which  ought  always  to  follow  the  moon,  and  flow  from  east  to 
west ;  but  to  allow  the  tides  their  full  motion,  the  ocean  in  which 
they  are  produced  ought  to  extend  from  east  to  west  at  least  90 
degrees,  or  6255  English  miles  ;  because  that  is  the  distance  be- 
tween the  places  where  the  water  is  most  raised  and  depressed 
by  the  moon.  Hence  it  appears  that  it  is  only  in  the  great  oceans 
that  the  tide  can  flow  regularly  from  east  to  west ;  and  hence  we 
also  see  why  the  tides  in  the  Pacific  Ocean  exceed  those  in  the 
Atlantic,  and  why  the  tides  in  the  torrid  zone,  between  Africa  and 
America,  though  nearly  under  the  moon,  do  not  rise  so  high  as  in 
the  temperate  zones  northward  and  southward,  where  the  ocean 
is  considerably  wider.  The  tides  in  the  Atlantic,  in  the  torrid 
zone,  flow  from  east  to  west  till  they  are  stopped  by  the  conti- 
nent of  America  ;  and  the  trade  winds  likewise  continue  to  blow 
in  that  direction.  When  the  action  of  the  moon  upon  the  waters 
has  in  some  degree  ceased,  the  force  of  the  trade  winds,  in  a 
great  measure  prevents  their  return  towards  the  African  shores. 
The  waters  thus  accumulated*  in  the  gulf  of  Mexico,  return  to 
the  Atlantic  between  the  island  of  Cuba,  the  Bahama  islands,  and 
East  Florida,  and  form  that  remarkable  strong  current  called  the 
gulf  of  Florida. 

Newton's  discovery  of  the  law  of  gravitation  naturally  led  to 
the  true  origin  of  the  tides.  That  great  author  has  shown,  in  the 
third  book  of  his  Principia,  that  the  tides  are  produced  by  the 
disturbing  forces  of  the  sun  and  moon. 


*  To  show  that  an  accumulation  of  water  does  take  place  in  the  gulf  of  Mexico, 
a  survey  was  made  across  the  isthmus  of  Darien,  when  the  water  on  the  Atlantic 
was  found  to  be  14  feet  higher  than  the  water  on  the  Pacific  side.  Walker's 
Familiar  Philosophy,  Lecture  xi. 


Chap,  VII.        NATURAL  CHANGES  OF  THE  EARTH. 


97 


In  1740  the  theory  of  Newton  was  completely  developed  in  the 
Prize  Essays  of  M'Laurin,  Euler,  and  Bernoulli,  of  which  an  ex- 
cellent abstract  is  given  in  the  first  volume  of  Robinson's  Natural 
Philosophy. 

Laplace  is  the  only  mathematician  who  has  advanced,  in  this 
most  difficult  problem,  beyond  the  theory  of  Newton.  Instead 
of  the  statical  equilibrium  employed  by  Newton,  and  those  who 
have  followed  his  method,  Laplace  in  his  Mecanique  Celeste, 
considers  the  subject  in  its  true  point  of  view,  as  a  problem  in 
Hydrodynamics,  in  which  the  oscillations  of  the  waters  of  the 
ocean  are  to  be  derived  from  the  accelerating  forces,  by  the 
analytic  formulae  that  express  the  motion  of  fluids. 


CHAPTER  VII. 

Of  the  Natural  Changes  of  the  Earth,  caused  hy  Mountains, 
Floods,  Volcanoes,  and  Earthquakes, 

That  there  have  always  been  mountains  from  the  foundation 
of  the  world,  is  as  certain  as  that  there  have  always  been  rivers, 
both  from  reason  and  revelation* ;  for  they  were  as  necessary 
before  the  flood  for  every  purpose  as  they  are  at  present.  If  the 
earth  were  perfectly  level,  there  could  be  no  rivers,  for  water 
can  flow  only  from  a  higher  to  a  lower  place ;  and  instead  of  that 
beautiful  variety  of  hills  and  valleys,  verdant  fields,  forests,  &c. 
which  serve  to  display  the  goodness  and  beneficence  of  the  Deity, 
a  dismal  sea  would  corer  the  whole  face  of  the  earth,  and  render 
it  at  best  an  habitation  for  aquatic  animals  only. 

All  mountains  and  high  places  continually  decrease  in  height. 
Rivers  running  near  mountains  undermine  and  wash  a  part  of 
them  away,  and  rain  falling  on  their  summits  washes  away  the 
loose  parts,  and  saps  the  foundations  of  the  solid  parts,  so  that, 


♦  Four  rivers,  or  rather  four  branches  of  one  river,  are  expressly  mentioned  be- 
fore the  flood,  viz.  Pison,  Gihon,  Hiddekel,  and  the  Euhprates.  Genesis,  chap.  ii. 
And  in  the  7th  chapter  of  Genesis,  at  the  time  of  the  flood,  w^e  are  told  that  the 
fountains  of  the  great  deep  were  broken  up,  the  windows  of  heaven  were  opened, 
the  waters  prevailed  exceedingly  upon  the  earth,  and  all  the  high  hills  and  the 
mountains  were  covered. 

13 


98 


NATURAL  CHANGES  OF  THE  EARTH, 


Part  L 


in  the  course  of  time,  they  tumble  down.  Thus,  old  buildings 
on  the  tops  of  mountains  are  observed  to  have  their  foundations 
laid  bare  by  the  gradual  vv^ashing  avs^ay  of  the  earth.  In  plains 
and  valleys  we  find  a  contrary  effect;  the  particles  of  earth 
washed  down  from  the  hills  fill  up  the  valleys,  and  ancient  houses 
built  in  low  places  seem  to  sink.  For  the  same  reason  a  quan- 
tity of  mud,  slime,  sand,  earth,  &c.  which  is  continually  washed 
down  from  the  higher  places  into  the  rivers,  is  carried  by  the 
stream,  and  by  degrees  chokes  up  the  mouths  of  rivers,  especially 
when  the  soil  through  which  they  run  is  of  a  loose  and  rich  qual- 
ity. Thus,  the  water  of  the  river  Mississippi,  though  wholesome 
and  well  tasted,  is  so  muddy,  that  a  sediment  of  two  inches  of 
slime  has  been  found  in  a  half-pint  tumbler  of  it^  ;  this  river  is 
choked  up  at  the  mouth  with  the  mud,  trees,  &c.  which  are  wash- 
ed down  it  by  the  rapidity  of  the  current. 

The  highest  mountains  in  the  world  are  the  Andesf ,  in  South 
America,  which  extend  near  4300  miles  in  length,  from  the  prov- 
ince of  Quito  to  the  strait  of  Magellan  ;  the  highest,  called  Chim- 
bora^o,  is  said  to  be  20608  feet,  or  nearly  four  miles  above  the 
level  of  the  sea :  2400  feet  of  which,  from  the  summit,  are  al- 
ways covered  with  snow.  From  experiments  made  with  a  ba- 
rometerj  on  the  mountain  Cotopaxi,  another  part  of  the  Andes, 
it  appeared  that  its  summit  was  elevated  6252  yards,  or  upwards 
of  3  1-2  miles  above  the  surface  of  the  sea.  There  is  a  mountain 
in  the  island  of  Sumatra,  called  Ophir  by  the  Europeans,  the  sum- 
mit of  which  is  13842  feet  high :  the  Peak  of  Teneriffe,  in  the 
island  of  that  name,  is  said  to  be  13265  feet  or  upwards  of  2  1-2 
miles  high.  Mont  Blanc,  the  highest  mountain  in  Europe,  is 
15304  feet  above  the  level  of  the  sea.  These  irregularities,  al- 
though very  considerable  with  respect  to  us,  are  nothing  when 
compared  with  the  magnitude  of  the  globe.  Thus,  if  an  inch 
were  divided  into  one  huudred  and  ten  parts,  the  elevation  of 
Chimbora^o,  the  highest  of  the  Andes,  on  a  globe  of  eighteen 
inches  in  diameter,  would  be  represented  by  one^  of  these  parts. 


*  Morse's  American  Geography. 

•j-  Perhaps  the  Himalaya  mountains  are  an  exception,    See  the  JsTote,  page  5S. 

X  The  quicksilver  in  a  barometer  falls  about  one-tenth  of  an  inch  every  32  yards 
of  height;  so  that,  if  the  quicksilver  descend  three-tenths  of  an  inch  in  ascending  a 
hill,  the  perpendicular  height  of  that  hill  will  be  96  yards.  This  method  is  hable  to 
error.  See  the  causes  M^hicii  affect  the  accuracy  of  Barometrical  experiments,  in 
the  Edinburgh  Philosophical  Transactions,  by  Mr.  Playfair;  also  in  Keith's  Trig- 
onometry, fourth  edition,  page  97. 

§  See  the  note  (chap.  III.  page  72)  of  the  figure  of  the  Earth. 


Chap»  VII.  BY  MOUNTAINS,  FLOODS,  &C. 


99 


Hence,  the  earth,  which  appears  to  be  crossed  by  the  enor- 
mous height  of  mountains,  and  cut  by  the  valleys  and  the  great 
depth  of  the  sea,  is  nevertheless,  with  respect  to  its  magnitude, 
only  very  slightly  furrowed  with  irregularities,  so  trifling  indeed 
as  to  cause  no  difference  in  its  figure. 

Having,  in  some  measure,  accounted  for  the  descending  of  the 
earth  from  the  hills,  and  filling  up  the  valleys,  stopping  the  mouths 
of  rivers,  &c.  which  are  gradual,  and  much  the  same  in  all  ages, 
the  more  remarkable  changes  may  be  reduced  to  two  general 
causes,  floods  and  earthquakes. 

The  real  or  fabulous  deluges  mentioned  by  the  ancients  may 
be  reduced  to  six  or  seven,  and  though  some  authors  have  en- 
deavoured to  represent  them  all  as  imperfect  traditions  of  the 
universal  deluge  recorded  in  the  sacred  writings,  the  Abbe 
Mann,*  from  whom  the  following  observations  are  extracted, 
does  not  doubt  but  that  they  refer  to  various  real  and  distinct 
events  of  the  kind. 

1.  The  submersion  of  the  Atlantis  of  Plato  probably  was  the 
real  subsidence  of  a  great  island  stretching  from  the  Canaries 
to  the  Azores,  of  which  those  groups  of  small  islands  are  the 
relics. 

2.  The  deluge  in  the  time  of  Cadmusf  and  Dardanus,  placed 
by  the  best  chronologists  in  the  year  before  Christ  1477,  is  said 
by  Diodorus  Siculus  to  have  inundated  Samothrace,  and  the 
Asiatic  shores  of  the  Euxine  Sea. 

3.  The  deluge  of  Deucalion,  which  the  Arundelian  marbles,J 
or  the  Parian  chronicles,  fix  at  1529  years  before  Christ,  over- 
whelmed Thessaly. 

4.  The  deluge  of  Ogyges,  placed  by  Acusilaus  in  the  year  an- 
swering to  1796  before  Christ,  laid  waste  Attica  and  Boeotia. 
With  the  poetical  and  fabulous  accounts  of  Deucalion's  flood  are 
mingled  several  circumstances  of  the  universal  deluge ;  but  the 
best  writers  attest  the  locality  and  distinctness  both  of  the  flood 
of  Deucalion  and  Ogyges. 


*  Vide  Nouveaux  Memoires  de  I'Academie  Imperiale  et  Royale  de  Sciences  et 
des  Belles  Lettres,  de  Brussels,  tome  premier,  1788. 

I  The  ancient  names  which  occur  here  may  all  be  found  in  Lempriere's 
Classical  Dictionary. 

%  Ancient  stones,  whereon  is  inscribed  a  chronicle  of  the  city  of  Athens  en- 
graven in  capital  letters,  in  the  island  of  Pares,  one  of  the  Cyclades,  264  years 
before  Christ.  They  take  their  name  from  Thomas,  Earl  of  Arundel,  who  procured 
them  from  the  East.  They  were  presented  to  the  University  of  Oxford  in  the  year 
1667,  by  the  Hon.  Henry  Howard,  afterwards  Duke  of  Norfolk,  grandson  to  the 
first  collector  of  them. 


100 


NATURAL  CHANGES  OF  THE  EARTH, 


Part  I. 


5.  Diodorus  Siculus,  after  Manetheo,  mentions  a  flood  which 
inundated  all  Egypt  in  the  reign  of  Osiris ;  but,  in  the  relations 
of  this  event,  are  several  circumstances  resembling  the  history  of 
Noah's  flood. 

6.  The  account  given  by  Berosus  the  Chaldean  of  an  universal 
deluge  in  the  reign  of  Xisuthrus,  evidently  relates  to  the  same 
event  with  the  flood  of  Noah. 

7.  The  Persian  Guebres,  the  Bramins,  Chinese,  and  Americans 
have  also  their  traditions  of  an  universal  deluge.  The  account  of 
the  deluge  in  the  Koran  has  this  remarkable  circumstance,  that 
the  waters  which  covered  the  earth  are  represented  as  proceed- 
ing from  the  boiling  over  of  the  cauldron,*  or  oven,  Tannoury 
within  the  bowels  of  the  earth :  and  that,  when  the  waters  sub- 
sided, they  were  swallowed  up  again  by  the  earth. 

The  Abbe  next  gives  a  summary  of  the  Scripture  account  of 
Noah's  flood,  and  points  out  very  clearly  that  part  of  the  waters 
came  from  the  atmosphere,  and  part  from  under  ground  agree- 
ably to  the  11th  verse  of  the  viith  chapter  of  Genesis. 

Earthquakes  are  another  great  cause  of  the  changes  made  in 
the  earth.  From  history,  we  have  numerous  instances  of  the 
dreadful  and  various  effects  of  these  terrible  phenomena.  Pliny 
has  not  only  recorded  several  extraordinary  phenomena  which 
happened  in  his  own  time,  but  has  likewise  borrowed  many 
others  from  the  writings  of  more  ancient  nations. 

1.  A  city  of  the  Lacedemonians  was  destroyed  by  an  earth- 
quake, and  its  ruins  wholly  buried  by  the  mountain  Taygetus 
falling  down  upon  them.f 

2.  In  the  books  of  the  Tuscan  learning  an  earthquake  is  re- 
corded, which  happened  within  the  territory  of  Modena,  when 
L.  Martins  and  S.  Julius  were  consuls,  which  repeatedly  dashed 
two  hills  against  each  other;  with  this  conflict  all  the  villages 
and  many  cattle  were  destroyed. 

3.  The  greatest  earthquake  mentioned  in  history  was  that 
which  happened  during  the  reign  of  Tiberius  Caesar  when  twelve 
cities  of  Asia  were  laid  level  in  one  night.J 

4.  The  eruption  of  Vesuvius,  in  the  year  79,§  overwhelmed 


*  This  circumstance  is  mentioned  here,  because  it  agrees  with  Mr.  Whitehurst's 
theory  of  the  earth ;  he  supposes  the  flood  was  occasioned  by  the  expansive  force 
of  fire  generated  at  the  centre  of  the  earth. 

t  Pliny's  Natural  History,  chap.  79. 

I  PHny,  chap.  84. 

§  Pliny  lost  his  hfe  by  this  eruption,  from  two  eager  a  curiosity  in  viewing  the 
flames. 


Vhap,  VII. 


BY  MOUNTAINS,  FLOODS,  &C. 


101 


the  two  famous  cities  of  Herculaneum*  and  Pompeii,  by  a  shower 
of  stones,  cinders,  ashes,  sand,  &:c.  and  totally  covered  them 
many  feet  deep,  as  the  people  were  sitting  in  the  theatre.  The 
former  of  these  cities  was  situated  about  four  miles  from  the  cra- 
ter, and  the  latter  about  six. 

By  the  violence  of  this  eruption,  ashes  were  carried  over 
the  Mediterranean  sea  into  Africa,  Egypt,  and  Syria ;  and  at 
Rome  they  darkened  the  air  on  a  sudden,  so  as  to  hide  the  face 
of  the  sun.f  ' 

5.  In  the  year  1533,  large  pieces  of  rock  were  thrown  to  the 
distance  of  fifteen  miles,  by  the  volcano  Cotopaxi  in  Peru.  J 

6.  On  the  29th  September  1535,  previous  to  an  eruption  near 
Puzzoli,  which  formed  a  new  mountain  of  three  miles  in  circum- 
ference, and  upwards  of  1200  feet  perpendicular  height,  the 
earth  frequently  shook,  and  the  plain  lying  between  the  lake 
Averno,  mount  Barbaro,  and  the  sea  was  raised  a  little  ;  at  the 
same  time  the  sea,  which  was  near  the  plain,  retired  two  hundred 
paces  from  the  shore.§ 

7.  In  the  year  1538,  a  subterraneous  fire  burst  open  the  earth 
near  Puzzoli,  and  threw  such  a  vast  quantity  of  ashes  and  pumice 
stones,  mixed  with  water,  as  covered  the  whole  country,  and  thus 
formed  a  new  mountain,  not  less  than  three  miles  in  circumfer- 
ence, and  near  a  quarter  of  a  mile  perpendicular  height.  Some 
of  the  ashes  of  this  volcano  reached  the  vale  of  Diana,  and  some 
parts  of  Calabria,  which  are  more  than  one  hundred  and  fifty 
miles  from  Puzzoli.  || 

8.  In  the  year  1538,  the  famous  town  called  St.  Euphemia,  in 
Calabria  Ulterior,  situated  at  the  side  of  the  bay  under  the  juris- 
diction of  the  knights  of  Malta,  was  totally  swallowed  up  with  all 
its  inhabitants,  and  nothing  appeared  but  a  fetid  lake  in  the  place 
of  it.m 

9.  A  mountain  in  Java,  not  far  from  the  town  of  Panacura,  in 
the  year  1586,  was  shattered  to  pieces  by  a  violent  eruption  of 
glowing  sulphur  (though  it  had  never  burnt  before,)  whereby  ten 
thousand  people  perished  in  the  underland  fields.** 


*  This  city  was  discovered  in  the  year  1736,  eighty  feet  below  the  surface  of 
the  earth  ;  and  some  of  the  streets  of  Pompeii,  &c.  have  since  been  discovered, 
t  Burnet's  Sacred  History,  page  85,  vol.  ii. 

I  Ulloa's  Voyage  to  Peru,  vol.  i.  p.  324. 

§  Sir  William  Hamilton's  Observations  on  Vesuvius. 

II  Ibid.  p.  128. 

IT  Dr.  Hooke's  Post.  p.  306. 

**  Varenius's  Geography,  vol.  i.  p.  160. 


102 


NATURAL  CHANGES  OP  THE  EARTH, 


Part  1. 


10.  In  the  year  1600,  an  earthquake  happened  at  Arquepa,  in 
Peru,  accompanied  with  an  eruption  of  sand,  ashes,  &c.  which 
continued  during  the  space  of  twenty  days,  from  a  volcano  break- 
ing forth ;  the  ashes  falling  in  many  places,  above  a  yard  thick, 
and  in  some  places  more  than  two,  and  where  least,  above  a  quar- 
ter of  a  yard  deep,  which  buried  the  corn  grounds  of  maize  and 
wheat.  The  boughs  of  trees  were  broken,  and  the  cattle  died  for 
want  of  pasture ;  for  the  sand  and  ashes  thus  erupted,  covered 
the  fields  ninety  miles  one  way,  and  one  hundred  and  twenty  an 
other  way.  During  the  eruption,  mighty  thunders  and  lightnings 
were  heard  and  seen  ninety  miles  round  Arquepa,  and  it  was  so 
dark  whilst  the  showers  of  ashes  and  sand  lasted,  that  the  inhab- 
itants were  obhged  to  burn  candles  at  mid-day.* 

11.  On  the  16th  of  June,  1628,  there  was  so  terrible  an  earth- 
quake in  the  island  of  St.  Michael,  one  of  the  Azores,  that  the  sea 
near  it  opened,  and  in  one  place  where  it  was  one  hundred  and 
sixty  fathoms  deep,  threw  up  an  island  ;  which  in  fifteen  days 
was  three  leagues  long,  a  league  and  a  half  broad,  and  360  feet 
above  the  water,  f 

12.  In  the  year  1631  vast  quantities  of  boiling  water  flowed 
from  the  crater  of  Vesuvius  previous  to  an  eruption  of  fire ;  the 
violence  of  the  flood  swept  away  several  towns  and  villages,  and 
some  thousands  of  inhabitants.  J 

13.  In  the  year  1632,  rocks  were  thrown  to  the  distance  of 
three  miles  from  Vesuvius.^ 

14.  In  the  year  1646,  many  of  those  vast  mountains,  the  Andes,|| 
were  quite  swallowed  up  and  lost.H 

15.  In  the  year  1692,  a  great  part  of  Port  Royal,  in  Jamaica, 
was  sunk  by  an  earthquake,  and  remains  covered  with  water 
several  fathoms  deep ;  some  mountains  along  the  rivers  were 
joined  together,  and  a  plantation  was  removed  half  a  mile  from 
the  place  where  it  formerly  stood.** 

16.  On  the  11th  January,  1693,  a  great  earthquake  happen- 
ed in  Sicily,  and  chiefly  about  Catania ;  the  violent  shaking  of 
the  earth  threatened  the  whole  island  with  entire  desolation. 
The  earth  opened  in  several  places  in  very  long  clefts,  some 


*  Dr.  Hooke's  Post.  p.  304. 

t  Sir  W.  Hamilton's  Observations  on  Vesuvius  and  ^tna,  p.  159. 
t  Ibid. 

§  Baddam's  Abridg.  Phil.  Trans,  vol.  ii.  p.  417. 

II  M.  Condamine  represents  these  mountains  and  the  Appenines  as  chains  of 
volcanoes.    See  his  Tour  through  Italy,  1755. 
ir  Dr.  Hooke's  Post.  p.  306. 
**  Lowthorp's  Abridg.  Phil.  Trans,  vol.  ii.  p.  417. 


Chap.  VII.  BY  MOUNTAINS,  FLOODS,  &C. 


103 


three  or  four  inches  broad,  others  Hke  great  gulfs.  Not  less  than 
59,969  persons  were  destroyed  by  the  falling  of  houses  in  different 
parts  of  Sicily.* 

17.  In  the  year  1699,  seven  hills  were  sunk  by  an  earthquake 
in  the  island  of  Java,  near  the  head  of  the  great  Batavian  river, 
and  nine  more  were  also  sunk  near  the  Tangarang  river.  Be- 
tween the  Batavian  and  Tangarang  rivers,  the  land  was  rent  and 
divided  asunder,  with  great  clefts  more  than  a  foot  wide.f 

18.  On  the  20th  of  November,  1720,  a  subterraneous  fire  burst 
out  of  the  sea  near  Tercera,  one  of  the  Azores,  which  threw  up 
such  a  vast  quantity  of  stones,  &c.  in  the  space  of  thirty  days,  as 
formed  an  island  about  two  leagues  in  diameter  and  nearly  circu- 
lar. Prodigious  quantities  of  pumice  stone,  and  half  broiled  fish, 
were  found  floating  on  the  sea  for  many  leagues  round  the  island.  J 

19.  In  the  year  1746,  Calloa,  a  considerable  garrison  town  and 
sea-port  in  Peru,  containing  5000  inhabitants,  was  violently  shaken 
by  an  earthquake  on  the  28th  of  October ;  and  the  people  had  no 
sooner  begun  to  recover  from  the  terror  occasioned  by  the  dread- 
ful convulsion,  than  the  sea  rolled  in  upon  them  in  mountainous 
waves,  and  destroyed  the  whole  town.  The  elevation  of  this  ex- 
traordinary tide  was  such  as  conveyed  ships  of  burden  over  the 
garrison  walls,  the  towers,  and  the  town.  The  town  was  razed 
to  the  ground,  and  so  completely  covered  with  sand,  gravel,  &c. 
that  not  a  vestige  of  it  remained. § 

20.  Previous  to  an  eruption  of  Vesuvius,  the  earth  trembles, 
and  subterraneous  explosions  are  heard  ;  the  sea  likewise  retires 
from  the  adjacent  shore,  till  the  mountain  is  burst  open,  then  re- 
turns with  impetuosity  and  overflows  its  usual  boundary.  These 
undulations  of  the  sea  are  not  peculiar  to  Vesuvius ;  the  earth- 
quake which  destroyed  Lisbon,  on  the  first  of  November,  1755, 
was  preceded  by  a  rumbling  noise,  which  increased  to  such  a  de- 
gree as  to  equal  the  explosion  of  the  loudest  cannon.  About  an 
hour  after  these  shocks,  the  sea  was  observed  from  the  high  grounds 
to  come  rushing  towards  the  city  like  a  torrent,  though  against 
the  wind  and  tide  ;  it  rose  forty  feet  higher  than  was  ever  known, 
and  suddenly  subsided.  At  Rotterdam,  the  branches  or  chande- 
liers in  a  church  were  observed  to  oscillate  like  a  pendulum  :  and 
we  are  told  it  is  no  uncommon  thing  to  see  the  surface  of  the 


*  Lowthorp's  Abridg.  Phil.  Trans,  vol.  ii.  pp.  408,  409. 
t  Ibid.  vol.  ii.  p.  419. 

X  Eames'  Abridg.  Phil.  Trans,  vol.  vi.  part  ii.  p.  203. 
§  Osborne's  Relation  of  Earthquakes. 


104 


NATURAL  CHANGES  OF  THE  EARTH, 


Part  1. 


earth  undulate  as  the  waves  of  the  sea  at  the  time  of  these  dread- 
ful convulsions  of  nature.* 

21.  The  last  eruption  of  Vesuvius  happened  in  July  1794,  be- 
ing the  most  violent  and  destructive  of  any  mentioned  in  history, 
except  those  in  79,  and  1631.  The  lava  covered  and  totally  de- 
stroyed 5000  acres  of  rich  vineyards,  and  cultivated  lands ;  and 
overwhelmed  the  town  of  Torre-del-Greco  ;  the  inhabitants, 
amounting  to  18,000,  fortunately  escaped  ;  and  the  town  is  now 
rebuilding  on  the  lava  that  covers  their  former  habitations.  By 
this  eruption  the  top  of  the  mountain  fell  in,  and  the  mouth  of 
Vesuvius  is  now  little  short  of  two  miles  in  circumference. 

Earthquakes  are  generally  supposed  to  be  caused  by  nitrous 
and  sulphureous  vapours,  inclosed  in  the  bowels  of  the  earth, 
which  by  some  accident  take  fire  where  there  is  little  or  no  vent. 
These  vapours  may  take  fire  by  fermentation,-]-  or  by  the  acciden- 
tal falhng  of  rocks  and  stones  in  hollow^  places  of  the  earth,  and 
striking  against  each  other.  When  the  matters  which  form  sub- 
terraneous fires  ferment,  heat,  and  inflame,  the  fire  makes  an  effort 
on  every  side,  and  if  it  does  not  find  a  natural  vent,  it  raises  the 
earth  and  forms  a  passage  by  throwing  it  up,  producing  a  volcano. 
If  the  quantity  of  substances  which  take  fire  be  not  considerable, 
an  earthquake  may  ensue  without  a  volcano  being  formed.  The 
air  produced  and  rarefied  by  the  subterraneous  fire,  may  also  find 
small  vents  by  which  it  may  escape,  and  in  this  case  there  will 
only  be  a  shock,  without  any  eruption  or  volcano.  Again,  all  in- 
flammable substances,  capable  of  explosion,  produce,  by  inflam- 
mation, a  great  quantity  of  air  and  vapour,  and  such  air  will  ne- 
cessarily be  in  a  state  of  very  great  rarefaction  :  when  it  is  com- 
pressed in  a  small  space,  like  that  of  a  cavern,  it  will  not  shake  the 
earth  immediately  above,  but  will  search  for  passages  in  order  to 
make  its  escape,  and  will  proceed  through  the  several  interstices 
between  the  different  strata,  or  through  any  channel  or  cavern 
which  may  afford  it  a  passage.  This  subterraneous  air  or  vapour 
will  produce  in  its  passage  a  noise  and  motion  proportionable  to 
its  force  and  the  resistance  it  meets  with  :  these  effects  will  con- 
tinue till  it  finds  a  vent,  perhaps  in  the  sea,  or  till  it  has  diminished 
its  force  by  expansion. 


*  See  the  Phil.  Trans,  respectmg  the  earthquake  on  the  first  of  November,  1755, 
vol.  xlix.  part  I. 

t  An  equal  quantity  of  sulphur  and  the  filings  of  iron  (about  10  or  15  lb.)  worked 
into  a  paste  with  water,  and  buried  in  the  ground,  will  burst  into  a  flame  in  eight  or 
ten  hours,  and  cause  the  earth  round  it  to  tremble. 


Chop.  VII. 


BY  MOUNTAINS,  FLOODS,  &LC. 


105 


Mr.  Whitehurst  imagines,  that  fire  and  water  are  the  principal 
agents  employed  in  these  dreadful  operations  of  nature*  and  that 
the  undulations  of  the  sea  and  the  earth,  and  the  oscillation  of 
pendulous  bodies,  are  phenomena  which  arise  from  the  expansive 
force  of  steam,  generated  in  the  internal  parts  of  the  earth  by 
means  of  subterraneous  fires :  the  force  of  steam  being  twenty- 
eight  timesf  greater  than  that  of  gunpowder,  viz.  as  14,000  is  to 


in  the  earth,  especially  in  the  neighbourhood  of  volcanoes,  from 
the  frequent  eruptions  of  boiling  water  and  steam,  in  various  parts 
of  the  world.  Dr.  Uno  Von  Troil,  in  his  Letters  on  Iceland,  has 
recorded  many  curious  instances.  "  One  sees  here,"  says  he, 
"  within  the  circumference  of  half  a  mile,  or  three  English  miles, 
40  or  50  boiling  springs  together ;  in  some  the  water  is  perfectly 
clear,  in  others  thick  and  clayey :  in  some,  where  it  passes  through 
a  fine  ochre,  it  is  tinged  red  as  scarlet;  and  in  others,  where  it 
flows  over  a  paler  clay,  it  is  white  as  milk."  The  water  spouts 
up  from  some  of  these  springs  continually,  from  others  only  at 
intervals.  The  aperture  through  which  the  water  rose  in  the 
largest  spring  was  nineteen  feet  in  diameter,  and  the  greatest 
height  to  which  it  threw  a  column  of  water  was  ninety-two  feet. 
Previous  to  this  eruption  a  subterraneous  noise  was  frequently 
heard,  like  the  explosion  of  cannon ;  and  several  stones,  which 
were  thrown  into  the  aperture  during  the  eruption,  returned 
with  the  spouting  water.  <^ 


*  M.  Dolomieu  seems  to  be  of  the  same  opinion. 

t  The  force  of  steam  is  a  function  of  its  temperature,  and  therefore  cannot  be 
compared  to  force  of  gunpowder  unless  the  temperature  of  the  steam  be  given  : 
according  to  Robins,  the  force  of  inflamed  gunpowder  is  equal  to  the  pressure  of 
1000  atmospheres ;  but  by  the  experiments  and  calculations  of  Dr.  Hutton,  the 
force  of  gunpowder  is  much  greater  and  is  nearly  equal  to  the  pressure  of  2000  at- 
mospheres. 

i  Inquiry  into  the  Original  State  and  Formation  of  the  Earth,  chap.  xi.  page 


112. 


14 


106 


OF  THE  ATMOSPHERE,  &C. 


Part  I. 


Chapter  VIII. 


Of  the  Atmosphere,  Air,  Winds,  and  Hurricanes. 

The  earth  is  surrounded  by  a  thin  fluid  mass  of  matter,  called 
the  atmosphere  ;  this  matter  gravitates  towards  the  earth,  revolves 
with  it  in  its  diurnal  motion,  and  goes  round  the  sun  with  it  every 
year.  Were  it  not  for  the  atmosphere,  which  abounds  with 
particles  capable  of  reflecting  light  in  all  directions,  only  that 
part  of  the  heavens  would  appear  bright  in  which  the  sun  is  sit- 
uated and  the  stars  and  planets  would  be  visible  at  mid-day,-|- 
but,  by  means  of  an  atmosphere,  we  enjoy  the  sun's  light  (re- 
flected from  the  aerial  particles  contained  in  the  atmosphere)  for 
some  time  before  he  rises  and  after  he  sets ;  for,  on  the  21st  of 
June,  at  London,  the  apparent  day  is  9  m.  16  sec.  longer  than 
the  astronomical  day.J  This  invisible  fluid  extends  to  an  un- 
known height :  but  if,  as  astronomers  generally  estimate,  the  sun 
begins  to  enlighten  the  atmosphere  in  the  morning  when  he  comes 
within  18  degrees  of  the  horizon  of  any  place,  and  ceases  to  en- 
lighten it  when  he  is  again  depressed  more  than  18  degrees  below 
the  horizon  in  the  evening,  the  height  of  the  atmosphere  may 
easily  be  calculated  to  be  nearly  50  miles.§  Notwithstanding 
this  great  height  of  the  atmosphere,  it  is  seldom  sufficiently  dense 
at  two  miles  high  to  bear  up  the  clouds ;  it  becomes  more  thin 
and  rare  the  higher  we  ascend.    This  fluid  body  is  extremely 


*  Dr.  Keill,  Lect.  20. 

t  M.  de  Saussure,  when  on  the  top  of  Mont  Blanc,  which  is  elevated  5101  yards 
above  the  level  of  the  sea,  and  where  consequently  the  atmosphere  must  be  more 
rare  than  ours,  says,  that  the  moon  shone  with  the  brightest  splendour  in  the  midst 
of  a  sky  as  black  as  ebony ;  while  Jupiter,  rayed  like  the  sun,  rose  from  behind  the 
mountains  in  the  east.    Jlppend.  vol.  74,  Monthly  Review. 

X  See  KeiWs  Trigonometry,  fourth  edition,  page  302. 

§  Let  A  r  B  (Plate  III.  Fig.  5.)  represent  the  horizon  of  an  observer  at  a  ;  s  r  a 
ray  of  light  falling  upon  the  atmosphere  at  r,  and  making  an  angle  s  r  b  of  18  de- 
grees with  the  horizon  (the  sun  being  supposed  to  have  that  depression)  the  angle 
s  r  A  will  then  be  162  degrees.  From  the  centre  o  of  the  earth  draw  o  r,  and  it  will 
be  perpendicular  to  the  reflecting  particles  at  r ;  and,  by  the  principles  of  optics,  it 
will  likewise  bisect  the  angle  s  r  a.  In  the  right  angled  triangle  o  a  r,  the  angle 
o  r  a=81o,  a  o=(3982)  miles,  the  radius  of  the  earth.    Hence,  by  trigonometry, 

Sine  of  o  r  A,  81^    9.9946199 

Is  to  A  o,  (3982)   (3.6001013) 

As  radius,  sine  of  90'    10.0000000 

Is  to  o  r  (431.76)   (3.6054814) 

Now,  if  from  o  r=[4031.6,)  there  be  taken  o  v=:0  A=(3982,)  the  remainder 
V  r=(49.6)  miles  is  the  height  of  the  atmosphere. 


Chap.  VIII. 


OF  THE  ATMOSPHERE, 


107 


light,  being,  at  a  mean  density,  816  times  lighter  than  water  ;* 
it  is  likewise  very  elastic,  as  the  least  motion  excited  in  it  is 
propagated  to  a  great  distance :  it  is  invisible,  for  we  are  only 
sensible  of  its  existence  from  the  effects  it  produces.  It  is  capable 
of  being  compressed  into  a  much  less  space  than  what  it  naturally 
possesses,  though  it  cannot  be  congealed  or  fixed  as  other  fluids 
may ;  for  no  degree  of  cold  has  ever  been  able  to  destroy  its 
fluidity.  It  is  of  different  density  in  every  part  upwards  from 
the  earth's  surface,  decreasing  in  its  weight  the  higher  it  rises, 
and  consequently  must  also  decrease  in  density.  The  weight  or 
pressure  of  the  atmosphere  upon  any  portion  of  the  earth's  sur- 
face is  equal  to  the  weight  of  a  column  of  mercury  which  will 
cover  the  same  surface,  and  whose  height  is  from  28  to  31  inches : 
this  is  proved  by  experiment  on  the  barometer,  which  seldom 
exceeds  the  limits  above  mentioned.  Now,  if  we  estimate  the 
diameter  of  the  earth  at  7964f  miles,  the  mean  height  of  the  bar- 
ometer at  29  J  inches,  and  a  cubic  foot  of  mercury  to  weigh  13500 
ounces  avoirdupois,  the  whole  weight  of  the  atmosphere  will  be 
11522211494201773089  lbs.  avoirdupois,  and  its  pressure  upon 
a  square  inch  of  the  earth's  surface  14|  lbs. 

The  atmosphere  is  the  common  receptacle  of  all  the  effluvia  or 
vapours  arising  from  different  bodies,  viz.  of  the  steam  or  smoke 
of  things  melted  or  burnt ;  of  the  fogs  or  vapours  proceeding  from 
damp,  watery  places ;  of  steams  arising  from  the  perspiration  of 
whatever  enjoys  animal  or  vegetable  life,  and  of  their  putrescence 
when  deprived  of  it ;  also  of  the  effluvia  proceeding  from  sul- 
phureous, nitrous,  acid,  and  alkaline  bodies,  &c.  which  ascend  to 
greater  or  less  heights  according  to  their  specific  gravity.  Hence 
the  difficulty  of  determining  the  true  composition  of  the  atmos- 
phere.   Chemical  writers,J  however,  have  endeavoured  to  show 


*  Dr.  Thomson's  Chemistry,  vol.  iv.  page  7,  edition  of  1810. 

■j-  The  diameter  of  the  earth  in  inches  will  be  504599040  ;  and  the  diameter  with 
the  atmosphere  504599099  inches,  the  difference  between  the  cubes  of  these  diam- 
eters multiplied  by  -5236  gives  23597489140125231287-3564  cubic  inches  in  the  at- 
mosphere. Now,  if  1728  cubic  inches  weigh  13500  ounces,  as  stated  by  Dr.  Thom- 
son, page  6,  vol.  iv.  of  his  Chemistry,  the  weight  of  the  atmosphere  will  be  deter- 
mined as  above.  If  the  square  of  the  diameter  504599040  be  multiplied  by  3.1416, 
the  product  will  give  the  superficies  of  the  earth,  =  799914792576284098.56  square 
inches ;  and  if  the  weight  of  the  atmosphere  be  divided  by  these  superficies,  the 
quotient  will  be  14.4  lbs.  =  14  2-5  lbs.,  the  pressure  of  the  atmosphere  on  every 
square  inch  of  the  earth's  surface.  The  pressure  of  the  atmosphere  on  a  square 
inch  of  surface,  may  likewise  be  found  by  experiments  made  with  the  air-pump,  or 
by  weighing  a  column  of  mercury  whose  base  is  one  inch  square,  and  height  29^ 
inches. 

I  Dr,  Thomson's  Chemistry,  page  34,  vol.  iv.  edition  of  1810.   . 


108 


OF  THE  ATMOSPHERE,  &C. 


Part  I. 


that  it  consists  chiejly  of  three  distinct  elastic  fluids,  united  to- 
gether by  chemical  affinity ;  namely,  air,  vapour,  or  water,  and 
carbonic  acid  gas:*  differing  in  their  proportion  at  different 
times  and  in  different  places  ;  but  the  average  proportions  of 
each,  supposing  the  whole  atmosphere  to  be  divided  into  100 
equal  parts,  is  given  by  Dr.  Thomson  as  follows  : 

98^Vair, 

1      vapour  or  water, 
-iV  carbonic  acid. 


100 


Hence  it  appears,  that  the  foreign  bodies  which  are  mixed  or 
united  with  the  air  in  the  atmosphere  are  so  minute  in  quantity, 
when  compared  with  it,  that  they  have  no  very  sensible  influence 
on  its  general  properties  ;  wherefore,  in  describing  the  mechanic- 
al properties  of  the  air,  in  the  succeeding  parts  of  this  chapter, 
no  attention  is  paid  to  its  component  parts  in  a  chemical  point  of 
view;  but  wherever  the  word  air  occurs,  common  or  atmospheric 
air  is  always  meant.  It  may,  however,  be  proper  to  remark  here, 
that  from  variousf  experiments,  chemists  have  inferred  that  if 
atmospheric  air  be  divided  into  100  parts,  21  of  those  parts  will 
be  vital  air,  and  79  poisonous ;  hence  the  vital  air  does  not  com- 
pose one-third  of  the  atmosphere. 

Air  is  not  only  the  support  of  animal  and  vegetable  life,  but  it 
is  the  vehicle  of  sound  ;  and  this  arises  from  its  elasticity  :  for  a 
body  being  struck  vibrates,  and  communicates  a  tremulous  mo- 
tion to  the  air  :  this  motion  acts  upon  the  cartilaginous  portion  of 
the  ear,  where  there  are  several  eminences  and  concavities 
adapted  to  convey  it  into  the  auditory  passage,  where  it  strikes 
on  the  membrana  tympani,  or  drum  of  the  ear,  and  produces  the 
sense  of  hearing. 


*  Gas  is  a  term  applied  by  chemists  to  all  permanently  elastic  fluids,  except  com- 
mon air ;  and  carbonic  acid  gas  is  what  was  formerly  called  jixed  air,  or  such  as 
extinguishes  flame,  and  destroys  animal  life. 

f  Dr.  Thomson,  vol.  iv.  page  20,  of  his  Chemistry,  says,  "  Whatever  method  is 
employed  to  abstract  oxygen  from  air,  the  result  is  uniform.  They  all  indicate 
that  common  air  consists  very  nearly  of  21  parts  of  oxygen  and  79  of  azote," 

21  oxygen  gas  (viz.  vital  air.) 

79  azotic  gas  (viz.  poisonous  air.) 


100 


Chap.  Vin.  OF  THE  ATMOSPHERE,  <^C. 


109 


From  the  fluid  state  of  the  atmosphere,  its  great  subtility  and 
elasticity,  it  is  susceptible  of  the  smallest  motion  that  can  be  ex- 
cited in  it ;  hence  it  is  subject  to  the  disturbing  forces  of  the  moon 
and  the  sun ;  and  tides  will  be  generated  in  the  atmosphere  simi- 
lar to  the  tides  in  the  ocean.  By  the  continual  motion  of  the  air, 
noxious  vapours,  which  are  destructive  to  health,  are  in  some 
measure  dispersed ;  so  that  the  air,  like  the  sea,  is  kept  from  pu- 
trefaction by  winds  and  tides. 

Air  may  be  vitiated,  by  remaining  closely  pent  up  in  any  place 
for  a  considerable  length  of  time  ;  and,  when  it  has  lost  its  vivify- 
ing spirit,  it  is  called  damp  or  fixed  air,  not  only  because  it  is  filled 
with  humid  or  moist  vapours,  but  because  it  deadens  fire,  extin- 
guishes flame,  and  destroys  life. 

If  part  of  the  vivifying  spirit  of  air,  in  any  country,  begins  to 
putrefy,  the  inhabitants  of  that  country  will  be  subject  to  an  epi- 
demical disease,  which  will  continue  until  the  putrefaction  is 
over :  and  as  the  putrefying  spirit  occasions  this  disease,  so,  if  the 
diseased  body  contribute  towards  the  putrefying  of  the  air,  then 
the  disease  will  not  only  be  epidemical,  but  pestilential  and  con- 
tagious. 

The  air  will  press  upon  the  surfaces  of  all  fluids,  with  any  force, 
without  passing  through  them  or  entering  into  them ;  so  that  the 
sofest  bodies  sustain  this  pressure  without  suffering  any  change 
in  their  figure,  and  the  most  brittle  bodies  bear  it  without  being 
broken.  Thus  the  weight  of  the  atmosphere  presses  upon  the 
surface  of  water,  and  forces  it  up  into  the  barrel  of  a  pump.  It 
likewise  keeps  mercury  suspended  at  such  a  height,  that  its  weight 
is  equal  to  the  pressure,  and  yet  it  never  forces  itself  through  the 
mercury  into  the  vacum  above. 

Another  property  of  the  air  is,  that  it  is  expanded  by  heat,  and 
condensed  or  contracted  by  cold :  hence  the  fire  rarefying  the 
air  in  the  chimneys,  causes  it  to  ascend  the  funnels ;  while  the 
air  in  the  room,  by  the  pressure  of  the  atmosphere,  is  forced  to 
supply  the  vacancy,  and  rushes  into  the  chimney  in  a  constant 
torrent,  bearing  the  smoke  into  the  higher  regions  of  the  atmos- 
phere. In  large  cities,  in  the  winter,  where  there  are  many  fires, 
people,  and  animals,  the  air  is  considerably  more  rarefied  than  in 
the  adjoining  country;  for  which  reason,  continual  currents  of 
colder  air  rush  in  at  all  the  exterior  streets,  bearing  up  the  atten- 
uated and  contaminated  air  above  the  tops  of  the  houses  and 
the  highest  buildings,  and  supplying  their  place  with  air  of  a 
more  salubrious  quality.  The  more  extensive  winds  owe  their 
origin  to  the  heat  of  the  sun ;  this  heat  acting  upon  some  part  of 
the  air  causes  it  to  expand,  and  become  lighter,  and  consequently 


110 


OF  THE  ATMOSPHERE,  (fec. 


Part  I. 


it  must  ascend ;  while  the  air  adjoining,  which  is  more  dense  and 
heavy,  will  press  forward  towards  the  place  where  it  is. rarefied. 
Upon  this  principle,  we  can  easily  account  for  the  trade-winds, 
which  blow  constantly  from  east  to  west  about  the  equator ;  for 
when  the  sun  shines  perpendicularly  on  any  part  of  the  earth,  it 
will  heat  and  rarefy  the  air  in  that  part,  and  cause  it  to  ascend ; 
while  the  adjacent  air  will  rush  in  to  supply  its  place,  and  conse- 
quently will  cause  a  stream  or  current  of  air  to  flow  from  all  parts 
towards  that  which  is  the  most  heated  by  the  sun.  But  as  the 
sun,  with  respect  to  the  earth,  moves  from  east  to  west,  the  com- 
mon course  of  the  air  will  be  from  east  to  west ;  and  therefore  at 
or  near  the  equator,  where  the  mean  heat  of  the  earth  is  the  great- 
est, the  wind  will  blow  continually  from  the  east ;  but  on  the  north 
side  of  the  equator  it  will  decline  a  little  to  the  north ;  and,  on 
the  south  side  of  the  equator  it  will  decline  to  the  south.  If  the 
earth  were  covered  with  water,  the  motion  of  the  wind  would 
follow  the  apparent  motion  of  the  sun,  in  the  same  manner  as  the 
motion  of  the  water  would  follow  the  motion  of  the  moon ;  but, 
as  the  regular  course  of  the  tides  is  changed  by  the  obstruction  of 
continents,  islands,  &c.  so  the  regular  course  of  the  winds  is  chang- 
ed by  high  mountains,  by  the  declination  of  the  sun  towards  the 
north  and  south,  by  burning  sands  which  retain  the  solar  heat  to 
an  incredible  degree,  by  the  falling  of  great  quantities  of  rain, 
which  causes  a  suden  condensation  or  contraction  of  the  air,  by 
exhalations  that  rise  out  of  the  earth  at  certain  times  and  places, 
and  from  various  other  causes.  Thus,  according  to  Dr.  Halley, 
between  the  3d  and  10th  degrees  of  south  latitude,  the  south-east 
trade- wind  continues  from  April  to  October ;  during  the  rest  of 
the  year  the  wind  blows  from  the  north-w^est ;  but  between  Suma- 
tra and  New-Holland  this  monsoon*  blows  from  the  south  during 
our  summer  months :  it  changes  about  the  end  of  September,  and 
continues  in  the  opposite  direction  till  April. 

Over  the  whole  of  the  Indian  Ocean,  to  the  northward  of  the 
third  degree  of  south  latitude,  the  north-east  trade-wind  blows 
from  October  to  April,  and  a  south-west  wind  from  April  to  Oc- 
toberf.  From  Borneo,  along  the  coast  of  Malacca,  and  as  far  as 
Ohina,  this  monsoon  in  our  summer  blows  nearly  from  the  south, 


*  The  regular  winds  in  the  Indian  seas  are  called  monsoons,  from  the  Malay 
word  moosin,  which  signifies  "  a  season."    Forest's  Voyage,  page  95. 

t  The  student  will  find  these  winds  represented  on  Adams'  globes,  by  arrows 
having  the  barbed  points  flying  in  the  direction  of  the  wind,  as  if  shot  from  a  bow  ; 
and,  where  the  winds  are  variable,  these  arrows  seem  to  hi  flying  in  all  directions. 


Chap.  I. 


OF  THE  ATMOSPHERE,  &C. 


Ill 


and  in  the  winter  from  north  by  east.  Near  the  coast  of  Africa, 
between  Mosambique  and  Cape  Guardafui,  the  w^inds  are  irregu- 
lar during  the  whole  year,  owing  to  the  different  monsoons  which 
surround  that  particular  place.  Monsoons  are  likewise  regular  in 
the  Red  Sea ;  between  April  and  October  they  blow  from  the 
north-west,  and  during  the  other  months  from  the  south-east,  keep- 
ing constantly  parallel  to  the  Arabian  coast.* 

On  the  coast  of  Brazil,  between  Cape  St.  Augustine  and  the 
island  of  St.  Catherine,  from  September  to  April  the  wind  blows 
from  the  east  or  north-east ;  and  from  April  to  September  it  blows 
from  the  south-west ;  so  that  monsoons  are  not  altogether  con- 
fined to  the  Indian  Ocean. 

On  the  coast  of  Africa,  from  Cape  Bajador,  opposite  to  the  Ca- 
nary Islands,  to  Cape  Verd,  the  winds  are  generally  north-west ; 
and  from  hence  to  the  island  of  St.  Thomas,  near  the  equator, 
they  blow  almost  perpendicular  to  the  shore. 

In  all  maritime  countries  of  any  considerable  extent,  between 
the  tropics,  the  wind  blows  during  a  certain  number  of  hours  from 
the  sea,  and  during  a  certain  number  from  the  land  ;  these  winds 
are  called  sea  and  land  breezes.  During  the  day,  the  air  above 
the  land  is  hotter  and  more  rare  than  that  above  the  sea ;  the 
sea  air  therefore  flows  in  upon  the  land,  and  supplies  the  place 
of  the  rarefied  air,  which  is  made  to  float  higher  in  the  atmos- 
phere ;  as  the  sun  descends,  the  rarefaction  of  the  land  air  is  di- 
minished, and  an  equilibrium  is  restored.  As  the  night  ap- 
proaches, the  denser  air  of  the  hills  and  mountains  (for  where 
there  are  no  hills,  there  are  no  sea  and  land  breezes)  falls  down 
upon  the  plains,  and  pressing  upon  the  air  of  the  sea,  which  has 
now  become  comparatively  lighter  than  the  land  air,  causes  the 
land  breeze. 

The  Cape  of  Good  Hope  is  famous  for  its  tempests,  and  the 
singular  cloud  which  produces  them :  this  cloud  appears  at  first 
only  like  a  small  round  spot  in  the  sky,  called  by  the  sailors  the 
Ox's  Eye,  and  which  probably  appears  so  minute  from  its  exceed- 
ingly great  height. 

In  Natolia,  a  small  cloud  is  often  seen,  resembling  that  at  the 
Cape  of  Good  Hope,  and  from  this  cloud  a  terrible  wind  f  issues, 
which  produces  similar  effects.  In  the  sea  between  Africa  and 
America,  especially  at  the  equator  and  in  the  neighbouring  parts, 
tempests  of  this  kind  very  often  arise,  and  are  generally  announced 


*  Bruce's  Travels,  \o\.  i.  chap.  iv. 

t  This  wind  seems  to  be  described  by  St.  Paul,  in  the  27th  chapter  of  the  Acts, 
by  the  name  of  the  Euroclydon. 


112 


OP  THE  ATMOSPHERE,  &C. 


Part  I. 


by  small  black  clouds.  The  first  blast  which  proceeds  from  these 
clouds  is  fiarious,  and  would  sink  ships  in  the  open  sea,  if  the  sail- 
ors did  not  take  the  precaution  to  furl  their  sails.  These  tempests 
seem  to  arise  from  a  sudden  rarefaction  of  the  air,  which  produces 
a  kind  of  vacuum,  and  the  cold  dense  air  rushing  in  to  supply  the 
place. 

Hurricanes,  which  arise  from  similar  causes,  have  a  whirling 
motion  which  nothing  can  resist.  A  calm  generally  precedes 
these  horrible  tempests,  and  the  sea  then  appears  like  a  piece  of 
glass ;  but,  in  an  instant,  the  fury  of  the  winds  raises  the  waves 
to  an  enormous  height.  When  from  a  sudden  rarefaction,  or 
any  other  cause,  contrary  currents  of  air  meet  in  the  same  point, 
a  whirlwind  is  produced. 

The  force  of  the  wind  upon  a  square  foot  of  surface  is  nearly  as 
the  square  of  the  velocity ;  that  is,  if  on  a  square  board  of  one 
foot  in  surface,  exposed  to  a  wind,  there  be  a  pressure  of  one 
pound,  another  wind,  with  double  the  velocity^  will  press  the 
board  with  a  force  of  four  pounds,  &:c.  The  following  table,  ex- 
tracted from  the  Philosophical  Transactions,  shows  the  velocity  and 
pressure  of  the  winds,  according  to  their  different  appellations. 


Velocity  of  the  wind. 


Miles  in  one 
hour. 


1 

2 
3 
4 
5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
60 
80 

100 


Feet  in  one 
second. 


1.47 
2.93 
4.40 
5.87 
7.33 
14.67 
22.00 
29.34 
36.67 
44.01 
51.34 
58.68 
66.01 
73.35 
88.02 
117.36 

146.70 


Perpendicular 
force  on  one 
square  foot  in 
pounds  avoir- 
dupois. 


.005 
.020 
.044 
.079 
.123 
.492 
1.107 
1.968 
3.075 
4.429 
6.027 
7.873 
9.963 
12.300 
17.715 
31.490 

49.200 


Common  appellations  of  the 
winds. 


Hardly  perceptible. 
Just  perceptible. 

Gentle  pleasant  wind. 

Pleasant  brisk  gale. 

Very  brisk. 

High  winds. 

Very  high. 

A  storm  or  tempest. 
A  great  storm. 
A  hurricane. 

{A  hurricane  that  tears 
up  trees,  and  carries 
buildings,&c.  before  it. 


Cliap.  IX. 


OF  VAPOURS,  FOGS,  CLOUDS,  &C. 


113 


CHAPTER  IX. 

Of  Vapours,  Fogs  and  Mists,  Clouds,  Dew  and  Hoar  Frost,  Rain, 
■Snow  and  Hail,  Thunder  and  Lightning,  Falling  Stars,  Ignus 
Fatuus,  Aurora  Borealis,  and  the  Rainbow. 

1.  Vapours  are  composed  of  aqueous  or  watery  particles, 
separated  from  the  surface  of  the  water  or  moist  earth  by  the  ac- 
tion of  the  sun's  heat;  whereby  they  are  so  rarefied  and  sepa- 
rated from  each  other,  as  to  become  specifically  lighter  than  the 
air,  and  consequently  they  rise  and  float  in  the  atmosphere. 

2.  Fogs  and  mists.  Fogs  are  a  collection  of  vapours  which 
chiefly  rise  from  fenny,  moist  places,  and  become  more  visible  as 
the  light  of  the  day  decreases.  If  these  vapours  be  not  dispersed, 
but  unite  with  those  that  rise  from  water,  as  from  rivers,  lakes, 
&LQ,.  SO  as  to  fill  the  air  in  general,  they  are  called  mists. 

3.  Clouds  are  generally  supposed  to  consists  of  vapours  ex- 
haled from  the  sea  and  land.*  These  vapours  ascend  till  they  are 
of  the  same  specific  gravity  as  the  surrounding  air ;  here  they 
coalesce,  and  by  their  union  become  more  dense  and  weighty. 
The  more  thin  and  rare  the  clouds  are,  the  higher  they  soar,  but 
their  height  seldom,  if  ever,  exceeds  two  miles.  The  generality 
of  clouds  are  suspended  at  the  height  of  about  a  mile  ;  sometimes, 
when  the  clouds  are  highly  electrified,  their  height  is  not  above 
seven  or  eight  hundred  yards.  The  wonderful  variety  in  the 
colours  of  the  clouds  is  owing  to  their  particular  situation  to  the 
sun,  and  the  different  reflections  of  his  light.  The  various  figure 
of  the  clouds  probably  proceeds  from  their  loose  and  voluble  tex- 
ture, revolving  in  any  form,  according  to  the  different  force  of 
the  winds,  or  from  the  electricity  contained  in  them. 


*  Dr.  Thomson,  in  vol.  iv.  of  his  Chemistry,  page  79,  &c.  edition  of  1810,  says, 
it  is  remarkable  that,  though  the  greatest  quantity  of  vapours  exist  in  the  lower 
strata  of  the  atmosphere,  clouds  never  begin  to  form  there,  but  always  at  some 
considerable  height.  The  heat  of  the  clouds  is  sometimes  greater  than  that  of  the 
surrounding  air.  The  formation  of  clouds  and  rain  is  neither  owing  to  the  satu- 
ration of  the  atmosphere,  nor  the  diminution  of  heat,  nor  the  mixture  of  airs  of  dif- 
ferent temperatures.  Evaporation  often  goes  on  for  a  month  together  in  hot 
weather,  especially  in  the  torrid  zone,  without  any  rain.  The  water  can  neither 
remain  in  the  atmosphere,  nor  pass  through  it,  in  a  state  of  vapour :  What  then 
becomes  of  the  vapour  after  it  enters  the  atmosphere?  what  makes  it  lay  aside  the 
new  form  which  it  must  have  assumed,  and  return  again  to  its  state  of  vapour,  and 
fall  down  in  rain  ?  Till  ij|;iese  questions  are  experimentally  answered.  Dr.  Thom- 
son concludes,  that  the  Wrmation  of  clouds  and  rain  cannot  be  accurately  account- 
ed for. 

15 


114 


OF  VAPOURS,  FOGS,  CLOUDS,  &C. 


Part  L 


The  general  colour  of  the  sky  is  blue,  and  this  is  occasioned 
by  the  vapours  which  are  always  mixed  with  the  air,  and  which 
have  the  property  of  reflecting  the  blue  rays,  more  copiously  than 
any  other.* 

4.  Dew.  When  the  earth  has  been  heated  in  the  day  time 
by  the  sun,  it  will  retain  that  heat  for  some  time  after  the  sun  has 
set.  The  air  being  a  less  dense  or  less  compact  substance,  will 
retain  the  heat  for  a  less  time :  so  that  in  the  evening  the  surface 
of  the  earth  will  be  warmer  than  the  air  about  it,  and  consequent- 
ly the  vapours  will  continue  to  rise  from  the  earth ;  but,  as  these 
vapours  come  immediately  into  a  cool  air,  they  will  only  rise  to 
a  small  height ;  as  the  rarefied  air  in  which  they  began  to  rise 
becomes  condensed,  the  small  particles  of  vapours  will  be  brought 
nearer  together.  When  many  of  these  particles  are  united,  they 
form  dew ;  and,  if  this  dew  freeze,  it  will  produce  hoar-frost. 

5.  Rain.  When  the  weight  of  the  air  is  diminished,  its  density 
will  likewike  be  diminished,  and  consequently  the  vapours  that 
float  in  it  will  be  less  resisted,  and  begin  to  fall,  and,  as  they  be- 
gin to  strike  upon  one  another  in  falling,  they  will  unite  and  form 
small  drops.  But  when  the  small  drops  of  which  a  cloud  con- 
sisted are  united  into  such  large  drops,  that  no  part  of  the  atmos- 
phere is  sufficiently  dense  to  produce  a  resistance  able  to  sup- 
port them,  they  will  then  fall  to  the  earth,  and  constitute  what  we 
call  rain.  If  these  drops  be  formed  in  the  higher  regions  of  the 
atmosphere,  many  of  them  will  be  united  before  they  come  to  the 
ground,  and  the  drops  of  rain  will  be  very  large. f  The  drops  of 
rain  increase  so  much  both  in  bulk  and  motion,  during  their  de- 
scent, that  a  bowl  placed  on  the  ground  would  receive,  in  a  show- 
er of  rain,  almost  twice  the  quantity  of  water  that  a  similar  bowl 
would  receive  on  a  neighbouring  high  steeple.J  The  mean  an- 
nual quantity  of  rain  is  greatest  at  the  equator,  and  decreases 
gradually  as  we  approach  the  poles.    Thus,  at 

Latitude.       Depth  of  rain. 

§Grenada,  West  Indies,       -  -  12°   0'  -  126  inches. 

St.  Domingo,  Cape  St.  Francois  -  19^  46'  -  120 

Calcutta      -          -          -  -  22  '  23'  -  81 

In  England  -          -          -  -  53^    0'  -  32 

Petersburgh           -          -  -  59^  16'  -  16 

*  Saussure,  Voyage  dans  les  Alpes,  vol.  iv.  p.  288. 

\  Dr.  Rutherford's  Natural  Philosophy,  vol.  ii.  chap.  10.  Signior  Beccaria, 
whose  observations  on  the  general  state  of  electricity  in  the  atmosphere  have  been 
very  accurate  and  extensive,  ascribes  the  cause  of  rain,  hail,  snow,  &c.  &c.  to  the 
effect  of  a  moderate  electricity  in  the  atmosphere. 

X  Mr.  Adam  Walker's  Familiar  Philosophy,  lect.  v.  page  215. 

§  Dr.  Thomson's  Chemistry,  vol.  iv.  page  83,  &.c.  edition  of  1810. 


Chap.  IX.  OF  VAPOURS,  fogs,  clouds,  &c. 


115 


On  the  contrary,  the  number  of  rainy  days  is  smallest  at  the 
equator,  and  increases  in  proportion  to  the  distance  from  it.  The 
number  of  rainy  days  is  often  greater  in  winter  than  in  summer; 
but  the  quantity  of  rain  is  greater  in  summer  than  in  winter. 
More  rain  falls  in  mountainous  countries  than  in  plains.  Among 
the  Andes,  it  is  said  to  rain  almost  perpetually,  while  in  the  plains 
of  Peru  and  Egypt,  it  hardly  ever  rains  at  all.  The  mean  an- 
nual quantity  of  rain  for  the  whole  globe  is  estimated  by  Dr. 
Thomson  at  34  inches  in  depth ;  hence  may  be  found  the  whole 
quantity  of  rain  that  falls  in  a  year  upon  the  whole  surface  of  the 
earth  and  sea,  in  the  same  manner  as  the  number  of  cubic  inches 
were  found  in  the  atmosphere,  in  chapter  VIII.  of  this  work. 
The  same  author  observes  that,  for  every  square  inch  of  the 
earth's  surface,  about  41  cubic  inches  of  water  is  annually  evap- 
orated ;  so  that  the  average  quantity  of  rain  is  considerably  less 
than  the  average  quantity  of  water  evaporated. 

6.  Snow  and  hail.  Snow  consists  of  such  vapours  as  are  fro- 
zen while  the  particles  are  small ;  for,  if  these  stick  together  after 
they  are  frozen,  the  mass  that  is  formed  out  of  them  will  be  of  a 
loose  texture,  and  form  little  flakes  or  fleeces,  of  a  white  substance, 
somewhat  heavier  than  the  air,  and  therefore  will  descend  in  a 
slow  and  gentle  manner  through  it.  Hail,  which  is  a  more  com- 
pact mass  of  frozen  water,  consists  of  such  vapours  as  are  united 
into  drops,  and  are  frozen  while  they  are  falling.* 

7.  Thunder  and  lightning.  It  has  been  already  observed, 
that  the  atmosphere  is  the  common  receptacle  of  all  the  effluvia 
or  vapours,  arising  from  different  bodies.  Now,  when  the  effluvia 
of  sulphureous  and  nitrousf  bodies  meet  each  other  in  the  air, 
there  will  be  a  strong  conflict,  or  fermentation  between  them, 
which  will  sometimes  be  so  great  as  to  produce  fire.J  Then,  if 
the  effluvia  be  combustible,  the  fire  will  run  from  one  part  to  an- 
other, just  as  the  inflammable  matter  happens  to  lie.  If  the  in- 
flammable matter  be  thin  and  light,  it  will  rise  to  the  upper  part 
of  the  atmosphere,  where  it  will  flash  without  doing  any  harm ; 
but  if  it  be  dense,  it  will  lie  near  the  surface  of  the  earth,  where, 
taking  fire,  it  will  explode  with  a  surprising  force,  and  by  its  heat 
rarefy  and  drive  away  the  air,  kill  men  and  cattle,  split  trees, 
walls,  rocks,  &c.  and  be  accompanied  with  terrible  claps  of  thun- 


*  Rutherford's  Philosophy,  vol.  ii.  chap.  10. 

t  Gunpowder,  the  effects  of  which  are  similar  to  thunder  and  lightning,  is  com- 
posed of  six  parts  of  nitre,  one  part  of  sulphur,  and  one  part  of  charcoal. 
X  Professor  Winkler's  Philosophy. 


116 


OF  VAPOURS,  FOGS,  CLOUDS,  &C. 


Part  I 


der.  The  effects  of  thunder  and  lightning  are  owing  to  the  sud- 
den and  violent  agitation  the  air  is  put  into,  together  with  the 
force  of  the  explosion.  Stones  and  bricks  struck  by  lightning, 
are  often  found  in  a  vitrified  state.  Signior  Beccaria  supposes 
that  some  stones  in  the  earth,  having  been  struck  in  this  manner, 
gave  rise  to  the  vulgar  opinion  of  the  thunder-bolt.  It  is  now 
generally  admitted  that  lightning  and  the  electrical  fluid  are  the 
same.* 

8.  The  falling  stars,  and  other  fiery  meteors,  which  are 
frequently  seen  at  a  considerable  height  in  the  atmosphere,  and 
which  have  received  different  names  according  to  the  variety  of 
their  figure  and  size,  arise  from  the  fermentation  of  the  effluvia 
of  acid  and  alkaline  bodies,  which  float  in  the  atmosphere.  When 
the  more  subtile  parts  of  the  cflfluvia  are  burnt  away,  the  viscous 
and  earthy  parts  become  too  heavy  for  the  air  to  support,  and  by 
their  gravity  fall  to  the  earth. 

The  disappearance  of  fiery  meteors  is  frequently  accompanied 
by  a  loud  explosion  like  a  clap  of  thunder,  and  heavy  stony  bodies 
have  been  observed  to  fall  from  them  to  the  earth.  Dr.  Thom- 
son-f  has  given  a  table  of  thirty-six  showers  of  stones,  with  the 
places  where  they  fell,  the  dates,  and  the  testimonies  annexed. J 

These  stoney  bodies,  when  found,  are  always  hot,  and  their  size 
differs  from  a  few  ounces  to  several  tons.  They  are  usually 
round,  and  always  covered  with  a  black  crust.  When  broken, 
they  appear  of  an  ash  grey  colour,  and  of  a  granular  texture,  like 
coarse  sand-stone.  These  substances  are  probably  concretions 
actually  formed  in  the  atmosphere,  but  in  what  manner  no  ra- 
tional account  has  yet  been  given.  Some  philosophers  conjecture 
that  meteoric  stone  are  projected  from  the  moon  by  volcanoes  ; 
the  velocity  necessary  for  this  projection  being  only  about  7000 
feet  per  second,  or  a  little  more  than  thrice  the  greatest  velocity  of  a 


*  Signior  Beccaria,  of  Turin,  observes  that  the  atmosphere  abounds  with  elec- 
tricity ;  and  if  a  cloud  which  is  positively  charged  (viz.  which  has  more  than  its 
natural  share  of  electrical  fluid)  pass  near  another  cloud  which  is  negatively 
charged  (viz.  which  has  less  than  its  natural  share  of  electrical  fluid),  they  will  at- 
tract each  other,  and  a  quick  deprivation  of  the  electrical  fluid  will  take  place :  the 
flash  is  called  Hghtning,  and  the  report  thunder;  (the  ensuing  rollings  are  only 
echoes  from  distant  clouds;)  the  water,  thus  deprived  of  its  usual  support,  falls 
down  in  impetuous  torrents, 

t  Chemistry,  edition  of  1810,  vol.  iv.  page  122. 

J  In  the  first  volume  of  the  Edinburgh  Philosophical  Journal  (1819)  page  221, 
&c.  is  given  an  "  account  of  meteoric  stones,  masses  of  iron,  and  showers  of  dust, 
red  snow,  and  other  substances,  which  have  fallen  from  the  heavens,  from  the  ear- 
liest period  down  to  1819." 


Chap,  IX.  OF  VAPOURS,  FOGS,  CLOUDS,  &C.  Ill' 

cannon  ball.  Others  imagine  that  these  stones  are  small  frag- 
ments of  terrestrial  comets,  which  sometimes  pass  through  our 
atmosphere,  and  have  their  surfaces  violently  heated  by  the  re- 
sistance of  the  air ;  in  consequence  of  which  small  portions  of 
the  comet  are  detached  from  its  surface,  and  precipitated  to  the 
earth. 

9.  Of  THE  IGNIS  FATUus,  commonly  called  Will-with-a-Whisp 
or  Jack  with-a- Lantern.  This  meteor,  like  most  others,  has  not 
failed  to  attract  the  attention  of  philosophical  inquirers.  Sir 
Isaac  Newton,  in  his  Optical  Queries,  calls  it  a  vapour  shining 
without  heat.  Various  accounts  of  it  may  be  seen  in  the  Phi- 
losophical Transactions.*  The  most  probable  opinion  is,  that  it 
consists  of  inflammable  air,-|-  or  oleaginous  matter,  emitted  from 
a  putrefaction  and  decomposition  of  vegetable  substances,  in 
marshy  grounds  ;  which  being  kindled  by  some  electric  spark,  or 
other  cause  unknown  to  us,  will  continue  to  burn  or  reflect  a  kind 
of  thin  flame  in  the  dark,  without  any  sensible  degree  of  heat, 
till  the  matter  which  composes  the  vapour  is  consumed.  This 
meteor  never  abounds  on  elevated  grounds,  because  they  do  not 
sufliciently  abound  with  moisture  to  produce  the  inflammable  air, 
which  is  supposed  to  issue  from  bogs  and  marshy  places.  It  is 
often  observed  flying  by  the  sides  of  hedges,  or  following  the 
course  of  rivers  ;  the  reason  of  which  is  obvious,  for  the  current 
of  air  is  greater  in  these  places  than  elsewhere.  These  meteors 
are  very  common  in  Italy  and  in  Spain.  Dr.  ShawJ  has  describ- 
ed a  remarkable  ignis  fatuus,  which  he  saw  in  the  Holy  Land, 
when  the  atmosphere  was  so  uncommonly  thick  and  hazy,  that 
the  dew  on  the  horses'  bridles  was  remarkably  clammy  and  unc- 
tuous. This  meteor  was  sometimes  globular,  then  in  the  form  of 
the  flame  of  a  candle,  presently  afterwards  it  spread  itself  so 
much  as  to  involve  the  whole  company  in  a  pale  harmless  light, 
and  then  it  would  contract  itself  again,  and  suddenly  disappear ; 
but,  in  less  than  a  minute,  it  would  become  visible  as  before,  and 
running  along  from  one  place  to  another  with  a  swift  proo;ressive 
motion,  would  again  expand  itself,  and  cover  a  considerable  space 
of  ground. 


*  Mr.  Ray  and  some  others  suppose  it  to  be  a  collection  of  glow-worms  flying 
together;  but  Dr.  Derham  refuted  this  opinion.    No.  411. 

I  Inflammable  air  may  be  made  thus  :  exhaust  a  receiver  of  the  air-pump,  let  the 
air  run  into  it  through  the  flame  of  the  oil  of  turpentine,  then  remove  the  cover  of 
the  receiver,  and  hold  a  lighted  candle  to  the  air,  it  will  take  fire,  and  burn  quicker 
or  slovi^er  according  to  the  density  of  the  oleaginous  vapour. 

+  Shaw's  Travels,  p.  363. 


118 


OP  THE  AURORA  BOREALIS. 


Part  L 


10.  Of  the  aurora  borealis,  or  northern  lights.  There 
have  been  various  opinions  and  conjectures  respecting  the  cause 
and  properties  of  these  extraordinary  phenomena  ;^  and  the  most 
probable  opinion  is,  that  they  arise  from  exhalations,  and  are  pro- 
duced by  a  combustion  of  inflammable  air,  caused  by  electricity. 
This  inflammable  air  is  generated  particularly  betw^een  the  tropics, 
by  many  natural  operations,  such  as  the  putrefaction  of  animal 
und  vegetable  substances,  volcanoes,  &c. ;  and  being  lighter  than 
any  other,  ascends  to  the  upper  regions  of  the  atmosphere,  and, 
by  the  motion  of  the  earth,  is  urged  towards  the  poles  ;  for  it  has 
been  proved  by  experiments  that  whatever  is  lighter,  or  swims 
on  a  fluid  which  revolves  on  an  axis,  is  urged  towards  the  extreme 
points  of  that  axis  if  hence  these  inflammable  particles  continually 
accumulate  at  the  poles,  and  by  meeting  with  heterogeneous 
matter  take  fire,  and  cause  those  luminous  appearances  frequently 
seen  towards  the  polar  regions.} 

In  high  latitudes  the  Auroras  Boreales  appear  with  the  greatest 
lustre,  and  extend  over  the  greatest  part  of  the  hemisphere,  vary- 
ing their  colours  from  all  the  tints  of  yellow  to  the  most  obscure 
russet.§  In  the  north-east  parts  of  Siberia,  Hudson's  Bay,  &c. 
they  are  attended  by  a  continued  hissing  and  cracking  noise 
through  the  air,  similar  to  that  produced  by  fire- works. || 

11.  Of  the  rainbow.  The  rainbow  is  the  most  beautiful 
meteor  with  which  we  are  acquainted :  it  is  never  seen  but  in 
rainy  weather,  where  the  sun  illuminates  the  falling  rain,  and  when 
the  spectator  turns  his  back  to  the  sun.    There  are  frequently  two 


*  Philosophical  Transactions,  Nos.  305,  310,  320,  347,  348,  349,  351,  352,  363, 
365,  368,  376,  385,  395,  398,  399,  402,  410,  418,  431,  and  433,  &c. 

f  See  Mr.  Kirwan's  account  of  the  Aurora  Borealis,  Irish  Phil.  Transactions  for 
1788,  page  70. 

X  We  have  very  few  accounts  of  the  Aurora  Australis,  or  Southern  Lights, 
owing  perhaps  to  the  want  of  observations  in  those  remote  parts  of  the  globe,  and 
a  proper  channel  of  information.  Captain  Cook,  in  his  second  voyage  towards  the 
south  pole,  says:  "(February  17th,  1773:)  We  observed  a  beautiful  phenomenon 
in  the  heavens,  consisting  of  long  columns  of  clear  white  light,  shooting  up  from 
the  heavens  to  the  eastward,  almost  to  the  zenith,  and  gradually  spreading  over  the 
whole  southern  part  of  the  sky.  Though  these  columns  were  in  most  respects 
similar  to  the  Aurora  Borealis,  yet  they  seemed  to  differ  from  them  in  being  always 
of  a  whitish  colour.  The  stars  were  sometimes  hid  by,  and  faintly  to  be  seen 
through,  the  substance  of  these  Aurora  Australes.  The  sky  was  generally  clear 
when  they  appeared,  and  the  air  sharp  and  cold,  the  thermometer  standing  at  the 
freezing  point ;  the  ship  being  in  latitude  58°  south. 

§  Dr.  Rees'  New  Cyclopaedia,  word  Aurora  Borealis. 

II  Philosophical  Transactions,  vol.  Ixxiv,  page  288. 


Chap.  IX. 


OF  THE  RAINBOW. 


bows  seen,  the  interior  and  exterior  bow.  The  interior  bow  is 
the  brightest,  being  formed  by  the  rays  of  hght  falling  on  the  up* 
per  parts  of  the  drops  of  rain  ;  for  a  ray  of  light  entering  the 
upper  part  of  a  drop  of  rain,  will,  by  refraction,  be  thrown  upon 
the  inner  part  of  the  spherical  surface  of  that  drop,  whence  it 
will  be  reflected  to  the  lower  part  of  the  drop,  where,  undergo- 
ing a  second  refraction,  it  will  be  bent  towards  the  eye  of  the 
spectator ;  hence  the  rays  which  fall  upon  the  interior  bow  come 
to  the  eye  after  two  refractions  and  one  reflection,  and  the  col- 
ours of  this  bow  from  the  upper  part  are  red,  orange,  yellow,  green, 
blue,  indigo,  and  violet.  The  exterior  bow  is  formed  by  the  rays 
of  hght  falling  on  the  lower  parts  of  the  drops  of  rain  ;  these  rays, 
like  the  former,  undergo  two  refractions,  iriz.  one  when  they  en- 
ter the  drops,  and  another  when  they  emerge  from  the  drops  to 
the  eye  ;  but  they  suflfer  two  or  more  reflections  in  the  interior 
surface  of  the  drops  ;  hence  the  colours  of  these  rays  are  not  so 
strong  and  well  defined  as  those  in  the  interior  bow,  and  appear 
in  an  inverted  order,  viz.  from  the  under  part  they  are  red,  or- 
ange,  yellow,  green,  blue,  indigo,  and  violet.  To  illustrate  this 
by  experiment,  suspend  a  glass  globe  filled  with  water  in  the  sun- 
sihine,  turn  your  back  to  the  sun,  and  view  the  globe  at  such  a 
distance  that  the  part  of  it  the  farthest  from  the  sun  may  appear 
of  a  full  red  colour,  then  will  the  rays  which  come  from  the  globe 
to  the  eye  make  an  angle  of  42  degrees  with  the  sun's  direct  rays  ; 
and  if  the  eye  remain  in  the  same  position,  and  another  person 
lower  the  glass  globe  gradually,  the  orange,  yellow,  green,  &c. 
colours,  will  appear  in  succession,  as  in  the  interior  bow.  Again, 
if  the  glass  globe  be  elevated,  so  that  the  side  nearest  to  the  sun 
may  appear  red,  the  rays  which  come  from  the  globe  to  the  eye 
will  make  an  angle  of  about  50  degrees  ;  then,  if  another  person 
gradually  raise  the  glass  globe,  while  the  spectator  remains  in  the 
same  position,  the  rays  will  successively  change  from  red  to  or- 
ange, green,  yellow,  &c.  as  in  the  exterior  bow.  These  observa- 
tions being  understood,  let  d  n  e  (Plate  IV.  Fig.  I.)  represent  a 
drop  of  rain  belonging  to  the  interior  bow,  s  <i  a  ray  of  light  fall- 
ing on  the  upper  part  of  the  drop  at  d ;  instead  of  the  ray  contin- 
uing its  direction  towards  f,  it  will  be  refracted  or  bent  towards 
n,  whence  part  of  it  (for  some  will  pass  through  the  drop)  will 
be  reflected  to  e,  making  the  angle  of  incidence  d  nk  equal  to 
the  angle  of  reflection  e  nk ;  instead  of  continuing  its  direction 
from  e  towards  /,  it  will,  by  emerging  out  of  the  water  into  the 
air,  be  again  refracted  to  the  eye  at  o.    But,  as  this  ray  of  light 


120 


OF  THE  RAINBOW. 


Part  1. 


consists  of  a  pencil*  of  rays,  some  of  which  are  more  refrangi- 
blet  than  others,  the  violet,  which  is  the  most  refrangible,  will 
proceed  towards  b,  and  the  red,  which  is  the  least  refrangible, 
will  proceed  towards  o.  Now,  if  the  eye  of  the  spectator  be 
so  placed  that  the  ray  of  light  falling  upon  it  has  been  once  re- 
flected, and  twice  refracted,  so  thut  o  e  shall  make,  with  the  solar 
ray,  s  an  angle  s  m  o  of  42''  2'J,  he  will  see  the  red  ray  in  the 
direction  o  e  m ;  and  if  the  eye  be  raised  to  b,  so  that  b  e  shall 
make,  with  the  solar  ray  s  d,  an  angle  b  r  s  of  40'  17'  the  violet 
ray  will  be  seen  in  the  direction  b  c  f  ;  the  red  ray  will  appear 
the  highest,  the  violet  the  lowest,  and  the  rest  in  order  according 
to  their  different  refrangibility,  as  in  the  interior  bow  {Fig.  2. 
Plate  IV.) ;  for  the  drop  of  water  descends  from  f  to  e.  What 
has  been  observed  of  one  drop  of  water,  will  be  true  in  an  infinite 
number  of  drops  ;  hence  the  interior  bow  is  composed  of  a  cir- 
cular arc,  whose  breadth  f  e,  is  proportioned  to  the  difference  be- 
tween the  least  and  most  refrangible  rays. 

To  explain  the  exterior  bow.  Let  c  t  nd  {Plate  IV.  Fig.  1.)  rep- 
resent a  drop  of  rain,  s  (i  a  ray  of  light  falling  upon  the  under 
part  of  it  at  d ;  instead  of  this  ray  continuing  its  direction  towards 
m,  it  will  be  refracted  to  n,  whence  part  of  it  will  pass  through  the 
drop,  and  the  rest  will  be  reflected  to  ^ ;  at  ^  a  part  of  it  will  again 
pass  through  the  drop,  and  the  remainder  will  be  reflected  to  c ; 
then  in  emerging  from  the  water  into  the  air,  instead  of  contin- 
uing the  direction  cz,  it  will  be  refracted  from  c  to  the  eye  at  o. 
But  as  this  ray  of  light,  like  that  in  the  interior  bow,  consists  of  a 


*  A  pencil  of  rays  is  a  portion  of  light  of  a  conical  form  diverging  or  proceeding 
&om  a  point;  or  tending  to  a  point,  in  which  case  the  rays  are  said  to  converge. 

f  Refrangibility  of  the  rays  of  light  is  their  tendency  to  deviate  from  their  natural 
course.  Those  rays  which  deviate  the  most  from  their  natural  course,  in  passing 
out  of  one  medium  into  another,  are  said  to  be  the  most  refrangible ;  and  those 
which  deviate  the  least  from  their  natural  course  are  the  least  refrangible.  Sir 
Isaac  Newton,  by  experiment,  found  the  red  rays  to  be  the  least  refrangible,  and 
the  violet  rays  the  most ;  and  those  rays  which  are  the  least  refrangible  are  like- 
wise the  least  reflexible. 

X  The  sine  of  incidence  and  refraction  of  the  least  refrangible  rays  out  of  water 
into  air,  is  as  3  to  4,  or  as  81  to  108;  and  the  most  refrangible,  as  81  to  109. 
Emerson's  Optics,  p.  92 — The  same  author,  at  page  237.  prob.  xxvi.  of  his  Optics, 
by  the  method  of  fluxions  or  increments,  and  using  the  numbers  above,  finds  that 
the  angle  which  the  emergent  ray  makes  with  the  incident  ray,  in  the  interior  bow, 
is  42°  2'  for  the  red,  and  40°  17'  for  the  violet ;  and  for  the  exterior  bow,  these  an- 
gles are  50°  57',  and  54°  7'.  The  investigations  are  here  omitted,  because  they 
cannot  be  rendered  intelligible  to  any  persons  but  mathematicians. 


Chap.  IX. 


OF  THE  RAINBOW. 


121 


pencil  of  rays  of  different  refrangibility,  the  red,  which  is  the  least 
refrangible,  will  proceed  towards  a  ;  and  the  violet,  which  is 
the  most  refrangible,  will  proceed  towards  o.  Now,  if  the  eye 
of  the  spectator  be  so  placed  that  the  ray  of  light  falling  upon  it 
has  been  twice  reflected,  and  twice  refracted,  so  that  o  o  shall 
make  with  the  solar  ray  s  o  an  angle  s  o  o  of  54°  7',  he  will  see 
the  violet  ray  in  the  direction  of  o  c  v ;  and  if  the  eye  be  raised 
to  A,  so  that  AO  shall  make  with  the  solar  ray  s  o  an  angle  s  o  a  of 
50°  57',  the  red  ray  will  be  seen  in  the  direction  a  c  r ;  the  violet 
ray  will  appear  the  highest,  and  the  red  ray  the  lowest,  and  the 
rest  in  order  according  to  their  different  refrangibility,  as  in  the 
exterior  bow  {Plate  lY.fig  2.)  for  the  drop  of  water  descends 
from  H  to  d.  The  same  observations  apply  to  an  infinite  number 
of  drops,  as  in  the  interior  bow. 

Hence,  if  the  sun  were  a  point,  the  breadth  of  the  exterior  bow 
would  be  (54"^  7'— 50°  57'  =)  3^  10',  that  of  the  interior  bow  (42° 
2' — 40°  17'=)  1°  45',  and  the  distance  between  them  (50°  57' — 
42^^  2  =)  8°  55' ;  but,  as  the  mean  diameter  of  the  sun  is  about 
32'  2",  the  breadths  of  the  bows  must  be  increased  by  this  quan- 
tity, and  their  distances  diminished ;  the  breadth  of  the  exterior 
bow  will  then  be  3°  42',  that  of  the  interior  bow  2°  17',  and  their 
distance  8°  23'.  The  greater  semi-diameter  of  the  interior  bow 
will  be  (42°  2'  -f  16',  the  sun's  semi-diameter  =)  42°  18',  and  the 
least  semi-diameter  of  the  exterior  bow  (50°  57' — 16'  the  sun's 
semi-diameter  =)  50°  41'. 

All  rainbows  are  arcs  of  equal  circles,  and  consequently  are 
equally  large,  though  we  do  not  always  see  an  equal  quantity  of 
them ;  for  the  eye  of  a  spectator  is  the  vertex  of  a  cone,  and  its 
circular  base  is  the  rainbow,  the  semi-diameter  of  which  (for  the 
interior  bow)  is  the  fixed  quantity  42°  18',  equal  to  an  angle  fop  ; 
and  as  sf  will  in  all  situations  be  parallel  to  op,  and  the  angle  sfo, 
equal  to  fop,  must  be  always  equal  to  42°  18',  it  is  evident  that 
as  s  rises,  f  and  p  will  sink ;  and  when  sf  makes  an  angle  of  42° 
18'  with  the  horizon,  of  will  coincide  with  oq,  and  the  interior 
bow  will  vanish ;  hence  the  interior  bow  cannot  be  seen  if  the 
sun's  altitude  exced  42°  18' :  again,  as  the  point  p  rises,  the  point 
s  will  sink,  and  when  op  coincides  with  oq,  sf  will  be  parallel  to 
the  horizon,  {viz.  the  sun  will  be  rising  or  setting,)  and  the  whole 
semi-diameter  of  the  rainbow  will  appear,  which  is  the  greatest 
part  of  it  that  ever  can  be  seen  on  level  ground  :  hence  half  a 
rainbow  is  tlie  most  that  can  be  seen  in  such  a  situation  ;  but  if 
the  observer  be  on  the  top  of  a  high  mountain,  such  as  the  Andes, 
with  his  back  to  the  sun,  and  if  it  rains  in  a  valley  before  him,  a 

16 


122 


OF  THE  RAINBOW. 


Part  I. 


whole  rainbow  may  be  seen,  forming  a  complete  circle.  The 
above  reasoning  is  equally  applicable  to  the  outer  bow ;  hence, 
as  the  sun  rises,  the  bows  sink,  and  when  its  altitude  exceeds  42° 
18',  the  interior  bow  cannot  be  seen,  and,  if  it  exceeds  (54°  7'  + 
16'  =)  54°  23',  the  exterior  bow  cannot  be  seen. 


PART  II, 


THE  ELEMENTARY  PRINCIPLES  OP  ASTRONOMY. 


ASTRONOMY  determines  the  altitudes,  distances,  magnitudes, 
and  orbits  of  the  heavenly  bodies  ;  describes  their  various  ap- 
parent and  real  motions,  their  periodical  revolutions,  eclipses 
or  occulations,  and  furnishes  us  with  a  rational  account  of  the 
various  phenomena  of  the  Heavens. 


CHAPTER  1. 

The  General  Appearance  of  the  Heavens, 

If,  on  a  clear  night,  we  stand  facing  the  south,  and  observe  the 
heavens,  they  will  appear  to  undergo  a  continual  change.*  Some 
stars  will  be  seen  ascending  from  the  east,  or  rising  ;  others  de- 
scending towards  the  west,  or  setting.  In  some  intermediate 
point  between  the  east  and  west,  each  star  will  reach  to  its  great- 
est height,  or,  will  culminate.  The  greatest  heights  of  the  several 
stars  will  be  different,  but  these  heights  will  all  be  attained  when 
the  stars  have  arrived  at  a  point  exactly  half  way  between  the 
east  and  the  west,  viz.  at  the  south. 

If  we  now  turn  our  backs  to  the  south,  and  observe  the  north, 
new  phenomena  will  present  themselves.  Some  stars  will  appear 
as  before,  rising,  attaining  their  greatest  heights,  and  setting; 
other  stars  will  be  seen,  that  never  set,  moving  with  different  de- 
grees of  velocity  ;  and  some  nearly  stationary. 

The  stars  which  never  set  appear  to  revolve  about  one  particu- 
lar star,  and  to  describe  circles  of  greater  or  less  circumferences, 
according  to  their  distances  from  that  star.  The  stationary  star 
is  called  the  Polar  star,  and  the  stars  which  revolve  round  it  at 
small  distances  are  called  the  circumsolar  stars. 

The  polar  star  which  appears  in  the  heavens  is  not  stationary, 
neither  is  it  situated  exactly  in  the  pole,  but  about  a  degree  and 


*  Exposition  du  Systeme  du  Monde,  p.  2. 


124 


THE  APPEARANCE  OP  THE  HEAVENS.  Part  11. 


three  quarters  from  it*  ;  that  is,  from  a  point  in  which,  if  a  star 
were  situated,  it  would  appear  perfectly  fixed. 

The  general  appearance,  therefore,  of  the  starry  heavens,  is 
that  of  a  vast  concave  sphere,  turning  round  two  imaginary  fixed 
points  diametrically  opposite  to  each  other,  the  one  in  the  north, 
the  other  in  the  south,  and  this  apparent  revolution  is  performed 
in  about  24  hours. 

Almost  all  the  stars  in  the  heavens  retain  towards  each  other 
the  same  relative  position,  they  neither  approach  towards,  nor 
recede  from  each  other,  and  are  therefore  called  fixed  stars. 
There  are,  however,  other  celestial  bodies,  having  the  appear- 
ance of  stars,  which  continually  change  their  places.  These  are 
called  planets. 

The  two  celestial  bodies  of  the  most  interesting  appearance, 
and  which  claim  our  greatest  attention,  are  the  sun  and  the  moon. 
These  vary  their  situations  from  day  to  day,  in  the  heavens  ; 
sometimes  they  appear  in  the  same  point  of  the  heavens,  and  at 
other  times  directly  opposite  to  each  other. 

The  moon  changes  her  figure  every  month,  in  which  time  she 
makes  a  complete  tour  round  the  heavens ;  and  though  she  appears 
to  rise  and  set  every  day  like  the  stars,  and  to  move  from  east  to 
west,  yet  her  apparent  motion  is  retarded,  and  when  compared 
with  any  particular  fixed  star  she  seems  to  go  backward  or  towards 
the  east :  that  is,  if  on  any  night  she  be  seen  in  conjunction  with  a 
particular  fixed  star,  the  next  night  she  will  appear  about  13°  to 
the  eastward  of  that  star,  the  succeeding  night  at  the  same  hour 
she  will  appear  26°  to  the  eastward  of  the  star,  and  so  on. 

The  common  phenomena  of  the  rising  and  setting  of  the  stars, 
and  their  apparent  revolution  from  east  to  west,  are  easily  ac- 
counted for,  on  the  simple  hypothesis  of  the  earth's  revolution  on 
its  axis  from  west  to  east  (See  Part  I.  Chap,  IV.)  ;  but  the  con- 
tinual change  of  place  which  the  sun,  the  moon,  and  the  planets 
undergo,  cannot  be  accounted  for  on  the  same  hypothesis,  nor  on 
the  supposition  that  the  whole  heavens  revolve  from  east  to  west 
in  24  hours. 

The  sun,  apparently,  moves  towards  the  stars,  which  set  after 
him,  and  from  those  which  set  before  him  :  that  is,  to  a  spectator 
in  the  northern  hemisphere,  facing  the  south,  his  apparent  motion 
is  from  the  right  hand  to  the  left. 

The  sun's  apparent  motion  from  west  to  east  with  respect  to 
the  fixed  stars,  will  adequately  explain  why  certain  remarkable 


*  Bee  the  note  to  Def.  4  p.  26. 


Chap.  I. 


THia  APPEARANCE   OF  THE  HEAVENS. 


125 


stars,  and  groups  of  stars  called  constellations,  are  seen  in  the 
south  at  different  hours  of  the  night  during  the  year.  For  the  hour 
depends  entirely  on  the  sun :  it  is  noon  when  he  is  in  the  south. 
Stars  which  are  directly  opposite  him  are,  therefore,  by  the  rota- 
tion of  the  earth  on  its  axis,  brought  to  the  meredian  at  midnight. 

But  the  stars  which  are  on  the  meredian  at  12  o'clock  one  night 
cannot  again  be  there  at  the  same  hour  on  the  succeeding  night ; 
for  the  sun* s  place  being  removed  a  little  to  the  east,  the  stars 
which  were  opposite  to  him  before  are  now  opposite  to  a  part  of 
the  heavens  a  little  to  the  westward  of  the  sun,  and  therefore  they 
will  come  to  the  meridian  a  little  before  midnight :  and,  on  each 
succeeding  night  they  will  come  to  the  meridian  by  greater  in- 
tervals before  midnight ;  so  that,  in  the  course  of  the  year  they 
are  all  successively  in  the  south,  though  sometimes  they  are  in- 
visible on  account  of  their  nearness  to  the  sun. 

The  moon  also  moves  among  the  stars  from  the  west  towards 
the  east,  more  rapidly  than  the  sun  appears  to  move  :  the  apparent 
motion  of  the  sun  arises  from  the  real  motion  of  the  earth  in  its 
orbit,  which  is  at  the  rate  of  about  one  degree  in  a  day,  {see  Def. 
61,  note,  page  36,)  whereas  the  motion  of  the  moon  is  about 
thirteen  degrees  in  a  day  {see  the  note,  page  91).  The  planets 
also,  if  observed  on  succeeding  nights,  will  appear  to  change 
their  places  amongst  the  fixed  stars,  though  when  viewed  from 
the  earth  they  will  not  always  appear  to  move  towards  the  east, 
but  sometimes  towards  the  west,  and  at  other  times,  for  several 
nights  together  they  will  appear  stationary. 

The  apparent  motion  towards  the  west,  and  the  stationary 
appearance,  are  merely  optical  and  illusory,  arising  from  the 
combination  of  the  earth's  motion  with  that  of  the  planet.  Viewed 
from  the  sun,  the  motion  of  the  planets  is  always  in  the  same  di- 
rection, and  they  never  appear  to  be  stationary. 

The  apparent  motion  of  the  sun,  and  the  real  motion  of  the 
moon  and  the  planets  from  west  to  east,  must  be  combined  with 
the  diurnal  motion  of  the  earth  on  its  axis  from  east  to  west.  The 
apparent  motion  of  the  stars  from  east  to  west  is  so  rapid  when 
compared  with  the  real  motion  of  the  planets  from  west  to  east, 
that  the  latter  motion  passes  unnoticed  by  inattentive  spectators. 


126 


TO  KNOW  THE  CONSTELLATIONS.  Part  XL 


CHAPTER  II. 

Of  the  Situation  of  the  principal  Constellations ^  and  the  Manner 
of  distinguishing  them  from  each  other. 

The  stars,  with  respect  to  their  apparent  splendour,  are  divided 
into  different  classes,  called  magnitudes.  The  brightest  are  called 
stars  of  the  first  magnitude ;  the  next  to  these  in  splendour,  stars 
of  the  second  magnitude,  and  so  on  to  those  which  are  just  per- 
ceptible to  the  naked  eye,  and  which  are  called  stars  of  the  sixth 
magnitude.  Those  which  cannot  be  discerned  without  the  as- 
sistance of  a  telescope,  are  called  Telescopic  Stars,  and  are 
divided  into  classes  of  the  seventh,  eighth,  &c.  magnitudes. 

The  ancients  divided  the  stars  into  different  groups  called  con- 
stellations (see  Def,  91),  and  gave  particular  names  to  each, 
which  names  the  greater  part  of  them  have  hitherto  retained. 
The  Pleiades  and  Orion  are  mentioned  in  the  sacred  writings  by 
Job,  and  Homer  and  Hesiod  describe  several  constellations  by 
names  which  are  now  in  general  use. 

A  knowledge  of  the  principal  constellations  in  the  heavens  will 
be  an  useful  acquisition  to  the  student,  and  this  may  be  obtained 
by  noting  the  time  when  they  come  to  the  meredian,  that  is,  to 
the  south. 

There  are  few  persons  who  are  unacquainted  with  the  seven 
(six)  stars  called  the  Pleiades,  or  the  beautiful  constellation  of 
Orion.^  The  Pleiades  come  to  the  meridian  of  London  about 
an  hour  before  Aldebaran,-|-  and  Orion  culminates  an  hour  after 
that  star ;  and,  since  the  diurnal  difference  of  time  of  a  star's  cul- 
minating is  nearly  equal  to  the  diurnal  difference  of  the  sun's 
right  ascension,  viz.  about  four  minutes ;  a  star  will  rise,  come  to 
the  meredian,  and  set,  nearly  four  minutes  earlier  every  day,  or 
about  two  hours  in  a  month. 

The  time  of  culminating  of  each  of  the  zodiacal  constellations 
is  given  in  the  following  table,  and  likewise  the  semi-diurnal  arc ; 
by  which  the  time  of  rising  and  setting  may  be  ascertained  suf- 
ficiently accurate  for  practice.  In  the  succeeding  description,  the 
principal  constellations  which  culminate  with  the  zodiacal  con- 
stellations are  pointed  out,  and  their  relative  positions  with  re- 
spect to  each  other  are  shown ;  so  that  the  time  of  their  coming 
to  the  meridian  may  be  easily  found  for  any  given  day  in  the  year. 


*  This  constellation  is  delineated,  agreeably  to  its  appearance  in  the  heavens, 
in  plate  V. 

t  The  time  of  this  star's  culminating  on  the  first  day  of  every  month,  is  given  in 
the  following  table. 


Chap.  11. 


TO  KNOW  THE  CONSTELLATIONS. 


127 


,H|iN  Ml'^  — —1^^  '-•k)*  cow        Ml**  rH|IM  '-iW 

05"— iw^t^oi^oocO'-HOOioas 


i-H  T}<  i>  CO  05       CM  (M       ..-J  t- 


ro  CO  OD  o  r- (  'M  -.^  o;)  »o  c-  05  CO 

— 1    r-H    n-<  (M    i-H  >-' 


lO  i>  o      CO      ^  lo      r-;  — t 

C".  C<1  r-^ 


too 


OirHr-((?qC0COG0O^— 'COlOCO 
1-H    (M    —  I-H 


.-Icq  '-Ic^  -|n  m^-Iw  -loi  r-l^  -1^ 

oor-<Tjicoi>0(M(roxoi>05CO 

<M  t-l^-(^-(r-Hr--,-H:^^ 


—1^       —In      i-i<m  -|-)i  f-.|^>- 

'-IC0COQ0O5(rqTtl>Ol>O:ir-Hr-l 
i-H   f-H  r-<  t— I   r-^  (M 


Ml^  1-]^  —1^  r-l^'  — 1(N  »-|'i'  — |*J<  — |rf 

C0x0Q0Or-HT:}Hi0b-O5  —  XiCO 

.-li-HrHi-«r-4-HCM01 


>-i(M  «i^  ,-1^  ,-1^ 


H<*      r-i|«  tJ(        HiN  M|^  >-<|cq      -In  -I^  1> 

l>O5(N'-HllO0DO5'-tC0rHC0 
r-H  rH  1—1  rH  (M  (M 


n3 
O 


d  .5 


O 

o  ^ 
o  ^ 
C3  O 


o  is  o  2  , 

.^=.^8'ii-g-.i 

=»•     CO  5»  O 


128 


TO  KNOW  THE  CONSTELLATIONS. 


Part  II. 


The  constellations  and  principal  stars  (visible  at  London)  which 
culminate  with  the  zodiacal  constellations  are  the  following,  count- 
ing from  the  horizon, 

1.  With  Aries  {a  Arietis.)  The  neck  of  Cetus,  Triangulum, 
Almaac  in  Andromeda,  the  head  of  Perseus,  and  the  feet  of  Cas- 
siopeia.— Mencar  in  Cetus,  Musca,  the  head  of  Medusa,  the  body 
of  Perseus,  and  the  tail  of  Camelopardalus,  culminate  three-quar- 
ters of  an  hour  after  Arietis. 

2.  With  Taurus  {Aldeharan.)  Part  of  Eridanus  and  Camelo- 
pardalus.— Algenih  in  Perseus  culminates  an  hour  and  a  quarter 
before  Aldebaran,  the  Pleiades  three-quarters  of  an  hour  before 
it,  Rigel  in  Orion,  and  Capella  in  Auriga,  about  half  an  hour  af- 
ter it. 

3.  With  Gemini  (Castor.)  Canis  Major,  Monoceros,  Canis 
Minor,  and  the  Lynx. — Sirius  culminates  three-quarters  of  an 
hour  before  Castor,  and  Procyon  about  six  minutes  after  Castor. 

4.  With  Cancer  {Acuhene.)  The  head  of  Hydra,  the  tail  of 
the  Lynx,  and  the  head  of  the  Great  Bear ;  none  of  which  are 
of  sufficient  importance  to  attract  the  student's  particular  atten- 
tion. 

5.  With  Leo  (Regulus.)  Part  of  Hydra,  Leo  Minor,  and  the 
shoulder  of  the  Bear.  The  pointers  in  the  Great  Bear  come  to 
the  meridian  (above  the  pole)  an  hour  after  Regulus. 

6.  With  Virgo  (Spica.)  The  middle  star  in  the  tail  of  the 
Great  Bear. — Coma  Berenices  and  Cor  Caroli  culminate  an  hour 
before  Spica;  and  Arcturus  in  Bootes  about  an  hour  after  Spica. 

7.  With  Libra  (a  on  the  ecliptic.)  The  left  leg  and  the  head 
of  Bootes. — The  head  of  the  serpent,  and  Corona  Borealis  cul- 
minate three-quarters  of  an  hour  after  a  in  Libra. 

8.  With  Scorpio  (Antares.)  The  left  arm  of  Serpentarius,  and 
the  club  and  body  of  Hercules. 

9.  With  Sagittarius  (the  star  in  the  bow  marked  ^.)  Scutum 
Sobieski,  Cerberus  in  the  left  hand  of  Hercules,  the  head  and 
body  of  Draco,  and  the  pole  of  the  ecliptic. — Vega  in  Lyra  cul- 
minates a  quarter  of  an  hour  after  ^in  Sagittarius. 

10.  With  Capricornus  (the  star  in  the  left  horn  marked  /9.) 
The  bow  of  Antinous,  Vulpecula  et  Anser,  and  the  neck  and  body 
of  Cygnus. — Altair  in  the  Eagle  comes  to  the  meridian  half  an 
hour  before  /3  Capricornus,  and  the  head  of  the  Dolphin  a  quar- 
ter of  an  hour  after  it. 

11.  With  Aquarius  (the  star  in  the  right  shoulder  marked  a.) 
The  feet  of  Pegasus,  the  Lizard,  and  the  head  of  Cepheus. — Fo- 


Chap.  II.  TO  KNOW  THE  CONSTELLATIONS, 


1^ 


malhout,  in  the  Southern  Fish,  culminates  three-quarters  of  an 
hour  after  a  Aquarius,  and  Markab  and  Scheat  in  Pegasus  an  hour 
after  it. 

12.  With  Pisces  (the  star  in  the  string  marked  a.)  The  head 
of  Aries,  Triangulum,  Almaac  in  Andromeda,  the  sword  of  Per- 
seus, and  the  feet  of  Cassiopeia. — a  in  the  head  of  Andromeda 
culminates  nearly  two  hours  before  a  in  Pisces,  and  Mirac  in  An- 
dromea  about  an  hour  before  it. 

If  the  student  observe  the  heavens  in  the  month  of  January^ 
about  ten  o'clock  in  the  evening,  when  the  stars  are  shining  very 
bright,  he  will  perceive  towards  the  south  the  Pleiades,  already 
mentioned ;  to  the  left  hand  of  which,  and  a  little  lower,  are  Al- 
debaran,  of  a  reddish  colour,  and  the  Hyades,  in  the  Bull  {delin- 
eated in  Plate  V.)  Three  stars  in  a  row  form  the  base  of  a  tri- 
angle, of  which  triangle  Aldebaran  is  situated  at  the  vertex.  Far- 
ther to  the  left  hand,  and  a  little  higher  than  the  Pleiades,  is  the 
remarkable  constellation  Auriga,  which  has  exactly  the  appear- 
ance of  the  figure  annexed. 


o 


The  highest  star  towards  the  left  hand  is  Capella,  the  star  marked 
^  and  y  is  situated  in  the  Bull's  north  horn,  and  also  in  the  right 
heel  of  Auriga. 

Imagine  a  hne  to  be  drawn  from  Capella  through  the  star 
marked  ^  y  towards  the  horizon,  and  it  will  pass  through  the  mid- 
dle of  the  constellation  Orion.  This  constellation  is  delineated 
in  Plate  V.,  and  is  so  brilliant  and  conspicuous  in  the  heavens  that 
its  figure  when  compared  with  the  plate  will  easily  be  known. 

The  three  stars  in  a  row  form  the  Belt,  and  the  largest  star  above 

17 


130 


TO  KNOW  THE  CONSTELLATIONS.  Part  II. 


the  Belt  towards  the  left-hand  is  Betelgeux,  a  star  of  the  first 
magnitude  in  Orion's  right  shoulder.  About  26°  from  Betelgeux, 
towards  the  left-hand  is  Procyon,  a  star  between  the  first  and 
second  magnitudes,  in  the  constellation  Canis  Minor.  Between 
Betelgeux  and  Procyon,  nearer  to  the  horizon,  is  Sirius,  easily 
distinguished  by  its  scintillation  and  lustre ;  these  three  stars  form 
an  equilateral  triangle. 

To  the  left  hand  of  Auriga,  and  at  about  the  same  distance 
from  Capella  as  Aldebaran  is,  you  will  perceive  Castor,  a  star  of 
the  first  magnitude  in  Gemini ;  and  near  it  towards  the  left-hand 
is  Pollux.  There  are  four  stars  in  a  line,  about  the  half-way  be- 
tween Betelgeux  and  Castor,  these  are  the  four  feet  of  Gemini. 
Castor  culminates  on  the  1st  of  February,  at  half-past  10  o'clock. 
Sirius  culminates  three-quarters  of  an  hour  before  Castor,  and 
Procyon  six  minutes  after. 

To  the  right  hand  of  Auriga,  and  above  the  Pleiades,  in  a  line 
with  Castor  and  Capella,  is  Algenib,  a  bright  star  in  the  breast  of 
Perseus,  and  farther  to  the  right  is  Almaac  in  Andromeda ;  these 
two  stars,  with  Algol  in  the  head  of  Medusa,  form  a  triangle,  of 
which  Algol  is  the  nearest  to  the  Pleiades.  Imagine  a  line  to  be 
drawn  from  the  Pleiades,  through  Algol,  and  it  will  pass  through 
Cassiopeia.  This  constellation  is  usually  described  by  the  figure 
of  an  inverted  chair  ;  but  there  are  five  bright  stars  in  it,  which 
resemble  the  capital  letter  W,  indifferently  made,  much  more 
than  a  chair. 

To  the  right  hand  of  the  Pleiades,  at  a  considerable  distance, 
viz.  about  22°  is  a  Arietis,  a  star  not  very  brilliant ;  a  line  drawn 
from  the  Pleiades  through  this  star  will  pass  through  Markab  in 
Pegasus.  The  constellation  Pegasus  is  very  remarkable,  the 
three  principal  stars  in  it,  with  the  head  of  Andromeda,  form  a 
large  square,  of  which  the  four  corner  stars  are  all  of  the  second 
magnitude.  The  highest  star  towards  the  right-hand  is  Scheat ; 
it  may  be  easily  known  by  a  kind  of  isosceles  triangle,  formed  by 
three  small  stars,  towards  the  right  hand  of  it ;  one  of  these  stars 
is  a  little  above  Scheat. 


Chap.  II.  TO  KNOW  THE  CONSTELLATIONS.  131 

o 


If  the  student  stand  facing  ^  jp 

the  north,  he  will  perceive  ivft^^^^^  O  ^5 

Ursa    Major,  or  the  Great  tv  ^ 

Bear,  the  most  conspicuous  ,<<^^  O 

constellation  in  the  heavens.  -v^^    \  ® 

It  is  visible  at  all  times  when  O 
there  are  any  stars  to  be  seen.  \ 
The   annexed  figure  repre-  \ 
sents  the  Great  Bear  when  \ 
below  the  pole.    Of  the  seven  \ 
brilliant  stars  in   the   Great  \^ 
Bear,  those  marked  a  and  /3  \ 
are.  called  the  pointers,  be-  \ 
cause  they  direct  the  eye  to  a     ^^A.  ^ccr  \ 
bright  star  at  P,  situated  about    ^      Q  '^^  • 

a  degree  and  three-quarters  SO 
from  the  pole  of  the  world,  ^   \  \ 

which  star,  from  its  vicinity  to  0  ' 

that  imaginary  point,  is  named  /  ^ 

the  polar-star. 

Ursa  Minor,  or  the  Little  Bear,  has  nearly  the  same  shape  as 
the  Great  Bear,  but  the  situation  is  inverted,  as  represented  by 
the  figure,  and  the  seven  stars  are  not  so  bright  as  those  in  the 
Great  Bear.  An  imaginary  line  drawn  through  the  centre  of  the 
square  of  the  Great  Bear,  perpendicular  to  the  sides,  will  point 
out  the  bright  star  marked  /3  in  the  square  of  the  Little  Bear. 


132 


TO  KNOW  THE  COKSTELLATIONS. 


Fak  II. 


These  constellations  will  assist  the  student  in  acquiring  a  knowl- 
edge of  the  situation  of  others. 

For  instance,  the  tail  of  Draco  lies  between  the  polar  star  and 
the  square  of  the  Great  Bear,  and  the  figure  extends  in  a  serpen- 
tine direction  towards  the  left-hand  to  a  considerable  distance, 
where  it  is  terminated  by  four  bright  stars  (in  the  head)  forming 
nearly  a  square.  An  imaginary  fine  drawn  through  <5  and  y  in 
Ursa  Major,  southward,  will  pass  through  the  brightest  star  in 
Leo  Minor,  and  through  Regulus  in  Leo  Major.  Regulus  is 
easily  distinguished,  being  the  southermost  of  four  bright  stars, 
resembling  the  letter  Z  inverted. 

By  the  foregoing  description,  with  the  assistance  of  a  celestial 
globe,  it  is  presumed  the  learner  mny  acquire  a  knowledge  of  the 
principal  constellations  which  appear  in  the  heavens  in  the  win- 
ter. Those  which  present  themselves  in  the  summer  are  less 
conspicuous,  but  many  of  them  may  be  distinguished  by  the  fol- 
lowing description. 

If  the  student  observe  the  heavens  about  ten  o'clock  in  the 
evening,  at  the  beginning  of  M.ay^  he  will  see  the  Great  Bear  near 
the  zenith,  above  the  pole.  To  the  right-hand  of  the  pointers 
in  the  Great  Bear,  and  near  the  horizon,  are  Castor  and  Pollux, 
already  described,  and  farther  to  the  right-hand  is  Auriga.  An 
imaginary  line  drawn  through  J"  and  7,  as  noticed  before,  will  pass 
through  Leo  Minor  and  through  Regulus,  and  being  continued  in 
the  same  direction  will  pass  through  the  heart  of  Hydra.  To  the 
right-hand  of  Cor  Hydrse,  near  the  horizon,  a  little  more  distant 
than  Regulus,  is  Procyon  in  Canis  Minor,  and  at  about  the  same 
distance,  on  the  left-hand,  is  Crater  the  Cup ;  beyond  which,  in 
the  same  diriction,  is  Corvus  the  Crow,  being  a  kind  of  square 
formed  by  four  principal  stars.  An  imaginary  line  drawn  through 
«  in  7  in  the  Great  Bear,  as  a  diagonal  to  the  square,  will  pass 
through  Cor  Caroli  near  Coma  Berenices,  and  through  Spica  Vir- 
ginis.  Spica  Virginis,  Arcturus  in  Bootes,  and  Deneb  in  the 
Lion's  tail,  form  an  equilateral  triangle,  in  which  Arcturus  is  the 
most  elevated,  and  Deneb  is  situated  towards  the  right-hand.  A 
line  connecting  the  first  and  third  stars  in  the  tail  of  the  Great 
Bear  will  pass  through  Corona  Borealis.  This  constellation  is 
of  an  oval  form,  and  is  composed  of  eight  stars,  three  of  which 
are  very  bright,  and  appear  close  to  each  other.  An  imaginary 
line  drawn  from  Arcturus  through  Corona  Borealis,  will  pass 
through  the  body  of  Hercules,  beyond  which,  in  the  same  direc- 
tion, is  the  bright  star  Vega  in  Lyra.  Below  Corona  Borealis  is 
Serpens,  the  Serpent ;  when  these  two  constellations  are  on  the 
meridian,  which  happens  about  three-quarters  of  an  hour  after 


Chap.  III.         THE  MOTION  OF  THE  FIXED  STARS, 


133 


the  culminating  of  a  in  Libra,  Arcturus  will  be  on  the  right-hand 
and  Vega  on  the  left.  Vega  in  Lyra,  Altair  in  the  Eagle,  and  the 
head  of  the  Dolphin,  form  an  isosceles  triangle,  of  which  Vega 
is  at  the  vertex.  Altair  is  easily  known,  being  the  middlemost  of 
the  three  bright  stars  situated  near  to  each  other  in  a  straight  line. 
The  Dolphin  lies  to  the  left-hand  of  the  Eagle,  and  is  composed 
of  about  five  stars,  four  of  which  appear  close  together.  Above 
the  Dolphin,  and  to  the  left  hand  of  Vega,  is  Cygnus,  a  remarka- 
ble constellation  in  the  milky  way,  in  the  form  of  a  large  cross, 
below  which  is  Pegasus  already  described. 

In  comparing  the  convex  surface  of  the  celestial  globe  with 
the  apparent  concavity  of  the  heavens,  the  student  will  observe 
that  the  figures  of  the  constellations  are  reversed  ;  those  which 
appear  to  the  right-hand  on  the  globe  are  to  the  left-hand  in  the 
heavens.  The  preceding  account  of  their  situations  refers  to  the 
heavens. 


CHAPTER  III. 

Of  the  Motion  of  the  Fixed  Stars  by  the  Precession  of  the  Equi- 
noxes, by  Aberration,  and  by  the  Nutation  of  the  EartKs  Axis 
their  proper  Motions,  Distance,  variable  Appearance,  <^c. 

It  has  already  been  shown  (Def  64.)  that  the  intersection  of 
the  ecliptic  with  the  equinoctial,  has  a  retrograde  motion  of  about 
50j  seconds  in  a  year,  and  that  a  revolution  of  the  equinoctial 
points  will  be  completed  in  about  525,791  years.  Now,  since  the 
equinoctial  changes  its  position  with  respect  to  the  ecliptic,  its 
axis  will  also  be  changeable,  and  its  poles,  in  the  course  of  25,791 
years,  will  describe  a  circular  path  in  the  heavens.  Hence  the 
longitude,  right  ascension,  and  declination  of  every  star  will  be 
variable,  and  consequently  the  pole  of  the  equinoctial  cannot  al- 
ways be  directed  to  the  same  star.  The  star  which  at  present 
is  nearest  to  the  north-pole  of  the  equinoctial  is  Alruccabah,  a  star 
of  the  second  magnitude  in  the  tail  of  the  Little  Bear ;  it  is  about 
a  degree  and  three  quarters  from  the  pole.  The  nearest  approach 
of  this  star  to  the  pole  will  be  when  its  longitude  is  90°  ;  it  will 
then  be  within  half  a  degree  of  the  pole,  and  this  will  happen  in 


134 


THE  MOTION  OF  THE  FIXED  STARS.  Part  II. 


the  year  2103,*  its  longitude  in  the  year  1800  being  85°  46'  10''. 
Since  the  fixed  stars  complete  a  revolution  about  the  axis  of  the 
ecliptic  in  25,791  years,  any  given  star  will  perform  half  a  revo- 
lution in  12,895|  years  ;  therefore  in  12,895  years  after  2103,  that 
is,  in  the  year  14,998,  the  present  polar  star  will  be  at  its  greatest 
distance  from  the  pole  of  the  equinoctial,  which  will  be  upwards 
of  forty-five  degrees.  In  the  year  of  the  world  1704,  the  star 
marked  a  in  Draco,  was  the  polar  star,  being  at  that  time  within 
one-sixth  of  a  degree  of  the  pole  of  the  equinoctial.  This  star 
lies  half  way  between  the  middle  star  in  the  tail  of  the  Great 
Bear  and  y  in  the  square  of  the  Little  Bear. 

The  aberration  of  the  fixed  stars  is  occasioned  by  the  velocity 
of  light,  combined  with  that  of  the  earth  in  its  orbit  {see  Def.  121.), 
by  which  each  star  apparently  decribes  an  ellipsis  about  its  mean 
place  in  a  year ;  the  longer  axis  of  this  ellipsis  is  about  40''.  The 
Nutation  arises  from  the  attraction  of  the  moon  upon  the  equato- 
rial parts  of  the  earth,  by  which  the  pole  of  the  equinoctial  de- 
scribes an  ellipsis  about  its  mean  place  as  a  centre.  This  ellipsis 
is  completed  in  a  revolution  of  the  moon's  nodes,  that  is,  in  18 
years  and  228  days ;  the  greater  axis  being  in  the  solstitial  co- 
lure  and  equal  to  19".  1,  and  the  less  axis  in  the  equinoctial  colure 
and  equal  to  14".2.f 

Dr.  Maskelyne  observes  J  that  many,  if  not  all  the  fixe^d  stars, 
have  small  motions  among  themselves,  which  are  called  their 
proper  motions ;  the  cause  and  laws  of  which  are  hid,  for  the 
present,  in  almost  equal  obscurity.  By  comparing  his  observa- 
tions with  others,  he  found  the  annual  proper  motion  of  the  fol- 
lowing stars,  in  right  ascension,  to  be,  of  Sirius, — 0".63  ;  of  Cas- 
tor,—0'\28  ;  of  Procyon,—0'\88 ;  of  Polhix—O'M ;  of  Regu- 
lus, — 0''.41 ;  of  Arcturus, — 1".4 ;  of  a  Aquilce  +  0''.57 ;  and  Sirius 
increased  in  north  Polar  distance  +r'.20  ;  Arcturus  +2  ".01. 

The  magnitudes  of  the  fixed  stars  will  probably  for  ever  remain 
unknown ;  all  that  we  can  have  any  reason  to  expect,  is  a  mere 
approximation  founded  on  conjecture.  From  a  comparison  of 
the  light  afforded  by  a  fixed  star,  and  that  of  the  sun,  it  has  been 
concluded  that  the  magnitudes  of  the  stars  do  not  differ  materially 
from  that  of  the  sun.    The  different  apparent  magnitudes  of  the 


*  60|"  :  1  year  :  :  90°— 35°  46'  10''  :  303  years,  which,  added  to  1800,  gives 
2103. 

f  Dr.  Mackay  on  the  Longitude,  vol.  i.  third  edition,  page  11. 
I  Explanation  of  the  Tables,  vol.  i.  of  his  Observations. 


Chap.  III.  THE  MOTION  OF  THE  FIXED  STARS. 


135 


stars  is  supposed  to  arise  from  their  different  distances,  for  the 
young  astronomer  must  not  imagine  that  all  the  fixed  stars  are 
placed  in  a  concave  hemisphere,  as  they  appear  in  the  heavens, 
or  on  a  convex  surface,  as  they  are  represented  on  a  celestial 
globe. 

From  a  series  of  accurate  observations  byDr.  Bradley  on  y  Dra- 
conis,  he  inferred  that  its  annual  parallax  did  not  amount  to  a  single 
second  ;  that  is,  the  diameter  of  the  earth's  annual  orbit,  which  is 
not  less  than  190  millions  of  miles,  w^ould  not  form  an  angle  at 
this  star  of  one  second  in  magnitude  ;  or,  that  it  appeared  in  the 
same  point  of  the  heavens  during  the  earth's  annual  course  round 
the  sun. 

The  same  author  calculates  the  distance  of  y  Draconis  from  the 
earth  to  be  400,000  times  that  of  the  sun,  or  38,000,000,000,000 
miles  :  and  the  distance  of  the  nearest  fixed  star  from  the  earth  to 
be  40,000  times  the  diameter  of  the  earth's  orbit,  or  7,600,000,- 
000,000  miles.  These  distances  are  so  immensely  great,  that  it 
is  impossible  for  the  fixed  stars  to  shine  by  the  light  of  the  sun  re- 
flected from  their  surfaces  :  they  must  therefore  be  of  the  same 
nature  with  the  sun,  and  like  him  shine  by  their  own  light. 

The  number  of  the  fixed  stars  is  almost  infinite,  though  the 
number  which  may  be  seen  by  the  naked  eye  in  the  whole  heavens 
does  not  exceed,  and  perhaps  falls  short  of  3000,*  comprehending 
all  the  stars  from  the  first  to  the  sixth  magnitude  inclusive  ;  but  a 
good  telescope,  directed  almost  indifferently  to  any  point  in  the 
heavens,  discovers  multitudes  of  stars  invisible  to  the  naked  eye. 
That  bright  irregular  zone,  the  milky  way,  has  been  very  care- 
fully examined  by  Dr.  Herschel ;  who  has,  in  the  space  of  a  quar- 
ter of  an  hour,  seen  116,000t  stars  pass  through  the  field  of  view 
of  a  telescope  of  only  15'  aperture. 


*  By  adding  up  the  numbers  of  stars  in  the  first  column  of  the  British  Catalogue 
given  at  pages  27,  28,  and  29,  the  sum  will  be  found  to  be  3457.    See  page  26. 

I  Vince's  Astronomy,  or  Philosophical  Transactions  for  1785,  vol.  Ixxv.  page  244. 
Dr.  Herschel  says,  "  in  the  most  crowded  part  of  the  milky  way  I  have  had  fields 
of  view  that  contained  no  less  than  588  stars,  and  these  were  continued  for  many 
minutes,  so  that  in  one  quarter  of  an  hour's  time  there  passed  no  less  than  1 16,000 
stars  through  the  field  of  view  of  my  telescope. — The  breadth  of  my  sweep  was  2-5 
26',  to  which  must  be  added  15'  for  the  two  semi-diameters  of  the  field.  Then 
putting  161'=a,  the  number  of  fields  in  15"  of  time;  7854=6,  the  proportion  of  a 
circle  to  1,  its  circumscribed  square ;  (p=s\nQ  of  74°  22'  the  polar  distance  of  the 
middle  of  the  sweep  reduced  to  the  present  time ;  and  588=s,  the  number  of  stars 
in  a  field  of  vievi',  we  have  a  ^  « 

 =116076  stars." 

h 


136 


THE  MOTION  OF  THE  FIXED  STARS.  Part  II. 


The  fixed  stars  are  the  only  marks  by  which  astronomers  are 
enabled  to  judge  of  the  course  of  the  moveable  ones,  because  they 
do  not  vary  their  relative  situations.  Thus,  in  contemplating  any 
number  of  fixed  stars,  which  to  our  view  form  a  triangle,  a  four- 
sided  figure,  or  any  other,  we  shall  find  that  they  always  retain 
the  same  relative  situation,  and  that  they  have  had  the  same  situ- 
ation for  some  thousands  of  years,  viz.  from  the  earliest  records  of 
authentic  history.  But  as  there  are  few  general  rules  without 
some  exceptions,  so  this  general  inference  is  likewise  subject  to 
restrictions.  Several  stars,  whose  situations  were  formerly  marked 
with  precision,  are  no  longer  to  be  found  ;  new  ones  have  also 
been  discovered,  which  w^ere  unknown  to  the  ancients  ;  while 
numbers  seem  gradually  to  vanish,  and  others  appear  to  have  a 
periodical  increase  and  decrease  of  magnitude.  Dr.  Herschel, 
in  the  Philosophical  Transactions  for  1783,  has  given  a  large  col- 
lection of  stars  which  were  formerly  seen,  but  are  now  lost,  to- 
gether with  a  catalogue  of  variable  stars,  and  of  new  stars. 

The  periodical  variation  of  Algol  or  /s  Persei,  is  about  two  days 
21  hours  ;  its  greatest  brightness  is  of  the  second  magnitude,  and 
least  of  the  fourth.  It  varies  from  the  second  magnitude  to  the 
fourth  in  about  3^  hours,  and  back  again  in  the  same  time,  retain- 
ing its  greatest  brightness  for  the  remainder  of  its  period. 

The  fixed  stars  do  not  appear  to  be  all  regularly  disseminated 
through  the  heavens,  but  the  greater  part  of  them  are  collected 
into  clusters ;  and  it  requires  a  large  magnifying  power,  with  a 
great  quantity  of  light,  to  distinguish  separately  the  stars  which 
compose  these  clusters.  With  a  small  magnifying  power,  and  a 
small  quantity  of  light,  they  only  appear  as  minute  whitish  spots, 
like  small  light  clouds,  and  thence  are  called  nebuloe.  Dr.  Her- 
schel has  given  a  catalogue  of  2000  nebuloe,  which  he  has  discov- 
ered, and  is  of  opinion  that  the  starry  heavens  are  replete  with 
these  nehulcR.  The  largest  nebula  is  the  milky  way,  already 
noticed  at  page  53. 

From  an  attentive  examination  of  the  stars  with  good  tele- 
scopes, many  which  appear  single  to  the  naked  eye,  have  been 


This  calculation  is  founded  upon  a  supposition  that  the  stars  were  equally  dis- 
seminated through  the  whole  field  of  view  of  the  telescope  ;  and  therefore  can  be 
considered  only  as  an  ingenious  approximation  to  the  truth. 


Chap,  IV.  THE  ASTRONOMICAL  QUADRANT. 


137 


found  to  consist  of  two,  three,  or  more  stars.  Dr.  Herschel,  by 
the  help  of  his  improved  telescopes,  has  discovered  nearly  700 
such  stars.  Thus  a  Herculis,  ^  Lyrce,  a  Geminorum,  y  Andro- 
medce,  f/-  Herculis,  and  many  others,  are  double  stars ;  v  LyrcB,  is 
a  triple  star ;  and  £  Lyrce,  /3  Lyrce,  a  Orionis,  and  |  LibrcBj  are 
quadruple  stars.* 


CHAPTER  IV. 

The  Method  of  measuring  the  Altitudes,  Zenith  Distances,  <^c.  of 
the  Heavenly  Bodies,  including  a  Description  of  the  Astronom- 
ical Quadrant,  Circular  Instrument,  and  Transit  Instrument 


It  is  of  importance  to  the  young  astronomer  to  know  in  what 
manner  the  altitudes  of  the  heavenly  bodies  are  determined ;  for 
which  reason  the  most  simple  instruments  for  that  purpose  are 
here  described.  This  description,  however,  must  be  considered 
as  contracted  and  imperfect,  since  the  various  adjustments  of  the 
instruments,  and  the  manner  of  using  them  to  advantage,  can  be 
acquired  only  by  practice. 

The  astronomical  quadrant 
is  generally  made  of  brass; 
the  arc  h  b  is  divided  into 
90  equal  parts,  called  de- 
grees, and  each  degree  is 
subdivided  into  smaller  parts, 
according  to  the  size  of  the 
instrument,  t  ^  is  a  tele-  O 
scope  moveable  about  a  cen- 
tre, c.  From  the  centre  c 
is  suspended  a  weight  p 
hanging  freely  in  the  direc- 
tion of  gravity,  or  perpendic- 
ularly to  the  earth's  surface, 
the  line  cp  is  called  a  plumb- 
line. 


*  Vince's  Astronomy,  chap.  xxiv. 

18 


138  THE  ASTRONOMICAL  QUADRANT.  Part  II. 


Now,  if  the  plane  of  the  instrument,  by  proper  adjustments, 
be  made  to  coincide  with  the  plane  of  the  meridian  of  any  place, 
and  the  plumb-line  cp  at  the  same  time  be  made  to  hang  exactly 
over  the  division  marked  90 ;  it  is  obvious,  that  if  the  telescope 
T  ^  be  directed  towards  the  star  s  in  the  plane  of  the  meridian, 
the  number  of  degrees  between  h  and  t  on  the  arc,  will  mark 
the  star's  altitude  o  s  on  the  meridian,  and  the  number  of  the  de- 
grees between  t  and  b  will  mark  its  zenith  distance  s  z  ;  for  the 
imaginary  quadrant  o  z  of  the  meridian  is  supposed  to  be  simi- 
larly divided  to  the  instrumental  quadrant  ii  b,  and  to  contain  90 
degrees  between  the  horizon  and  the  zenith.  If  the  star  be  in  the 
horizon  at  o,  the  telescope  will  coincide  with  h  o  or  be  parallel 
to  it ;  if  the  star  be  in  the  zenith  at  z,  the  telescope  will  coincide 
with  the  plumb-line  cp.  In  the  figure  annexed  the  telescope  is 
directed  towards  a  star  having  about  40  degrees  of  altitude.  The 
quadrant  may  be  placed  in  the  plane  of  any  other  vertical  circle 
as  well  as  in  that  which  passes  through  the  meridian,  and  then  it 
will  measure  altitudes  in  that  vertical  circle. 

When  the  quadrant  is  fixed  against  a  vertical  wall  in  the  plane  - 
of  the  meridian,  it  is  called  a  mural  quadrant.    Such  are  the 
quadrants  in  the  Royal  Observatory  at  Greenwich. 

The  astronomical  instrument  now  generally  used  is  an  im- 
provement upon  the  quadrant  here  described  ;  and  this  improve- 
ment consists,  chiefly,  in  putting  together  four  quadrants,  and 
thereby  forming  a  circular  instrument. 

The  figure  in  Plate  VI,  is  a  representation  of  a  small  model  of 
the  large  circles  used  in  observatories.*  The  vertical  circle  a  b 
is  formed  by  four  quadrants,  and  the  telescope  c  d  is  not  move- 
able on  the  arc  of  the  instrument  as  before,  but  is  attached  to  the 
circle,  and  moves  only  when  the  circle  itself  moves.  When  the 
telescope  is  placed  horizontally,  viz.  in  the  direction  a  b,  the  divi- 
sions marked  o  will  be  at  z  and  m.  If  the  telescope  be  directed 
to  any  star,  the  arc  of  the  circle  from  the  telescope  at  c  to  m  will 
show  the  zenith  distance  of  the  star,  and  the  arc  from  m  to  the 
division  marked  o  will  show  its  altitude  ;  if  the  instrument  be  sit- 
uated in  the  plane  of  the  meridian,  it  will  show  the  altitude  and 
polar  distance  of  any  star,  or  the  star's  dechnation  ;  for,  having 
the  latitude  of  a  place  given,  and  the  meridian  altitude  of  a  star, 
the  declination  of  that  star  is  readily  determined. 


*  This  figure  is  copied  from  a  new,  portable,  and  useful  instrument,  made  by 
Messrs.  W.  and  S.  Jones,  of  Holborn,  who  very  kindly  furnished  the  Author  with 
a  drawing  of  it,  from  which  drawing  the  plate  is  engraven. 


Chap,  V. 


OF  THE  SOLAR  SYSTEM. 


139 


The  vertical  circle  of  the  instrument  here  described  is  gradu- 
ated as  in  the  figure  ;  at  m  is  a  Nonius  scale,  w^ith  a  microscope, 
which  reads  off  to  one  minute  of  a  degree ;  the  slow  motion  of 
the  circle,  for  accuracy  of  observation,  is  produced  by  turning 
the  screw  at  g. 

The  achromatic  telescope  c  d  is  contrived  by  a  reflecting  eye- 
piece, to  admit  of  observations  conveniently  to  the  zenith.  The 
axis  of  the  vertical  circle  reverses  for  the  adjustment,  and  is  made 
level  by  the  small  suspended  spirit-level  l.  The  wires  of  the 
telescope  are  illuminated  at  night  by  a  small  reflector  placed  in 
the  inside  of  the  axis,  and  the  light  is  transmitted  through  the  axis 
by  means  of  a  small  lighted  lamp  occasionally  attached  to  it. 

The  base  of  the  instrument,  which  supports  the  vertical  circle, 
has  a  horizontal  motion,  the  slow  motion  of  which  is  produced  by 
turning  the  screw  at  o.  By  the  motion  of  the  horizontal  circle 
the  azimuths  of  the  celestial  objects  are  obtained,  and  this  circle 
is  placed  truly  horizontally  by  means  of  the  two  spirit-levels  s,  s ; 
the  screws  at  e,  e,  e,  are  for  the  purpose  of  fixing  the  base  in  its 
proper  position. 

When  the  vertical  circle  is  truly  placed  in  the  plane  of  the  me- 
ridian, the  vertical  wires  of  the  telescope  will  answer  the  purpose 
of  a  transit  instrument. 

By  the  assistance  of  this  instrument  the  altitude  of  the  sun's 
centre  may  be  observed  from  day  to  day,  and  this  altitude  will  be 
found  to  vary  continually  by  unequal  differences :  also  the  suc- 
cessive transits  of  the  fixed  stars  over  the  meridian  may  be  ascer- 
tained. 


CHAPTER  V. 
Of  the  Solar  System,    (Plate  II.  Fig.  1.) 

The  solar  system  is  so  called  because  the  sun  is  supposed  to 
be  situated  in  a  certain  point  termed  the  centre  of  the  system, 
having  all  the  planets  revolving  round  him  at  different  distances, 
and  in  different  periods  of  time.  This  is  likewise  called  the  Co- 
pernican  system. 


140 


OP  THE  SOLAR  SYSTEM. 


Part  II. 


I.  Op  the  Sun. 

The  sun  is  situated  near  one  of  the  foci  of  the  orbits  of  all  the 
planets,  and  revolves  on  its  axis  in  25  days  14  hours  4  minutes. 
This  revolution  is  determined  from  the  motion  of  the  spots  on 
its  surface,  which  first  make  their  appearance  on  the  eastern  ex- 
tremity, and  then  by  degrees  come  forv^^ards  towards  the  middle, 
and  so  pass  on  till  they  reach  the  western  edge,  and  then  disap- 
pear. When  they  have  been  absent  for  nearly  the  same  period 
of  time  which  they  were  visible,  they  appear  again  as  at  first,  fin- 
ishing their  entire  circuit  in  27  days  12  hours  20  minutes.* 

The  sun  is  likewise  agitated  by  a  small  motion  round  the  cen- 
tre of  gravity  of  the  solar  system,  occasioned  by  the  various  at- 
tractions of  the  surrounding  planets  ;  but,  as  this  centre  of  gravity 
is  generally  within  the  body  of  the  sun,-|-  and  can  never  be  at  the 
distance  of  more  than  the  length  of  the  solar  diameter  from  the 
centre  of  that  body,  astronomers  generally  consider  the  sun  as 
the  centre  of  the  system,  round  which  all  the  planets  revolve.  As 
the  sun  revolves  on  its  axis,  his  figure  is  supposed  not  to  be  strictly 
in  the  form  of  a  globe,  but  a  little  flatted  at  the  poles;  and 
that  his  axis  makes  an  angle  of  about  eight  degrees,  J  with  a  per- 
pendicular to  the  plane  of  the  earth's  orbit.  As  the  sun's  appa- 
rent diameter  is  greater  in  December  than  in  June,  it  follows  that 
the  sun  is  nearer  to  the  earth  in  our  winter  than  it  is  in  summer ; 
for  the  apparent  magnitude  of  a  distant  body  diminishes  as  the 
distance  increases.  The  mean  apparent  diameter  of  the  sun  is 
stated  to  be  32'  2" ;  hence,  taking  the  distance  of  the  sun  from 
the  earth  to  be  95  millions  of  miles  as  before  determined,^  its 


*  M.  Cassini  determined  the  time  which  the  sun  takes  to  revolve  on  its  axis  thus : 
the  time  in  which  a  spot  returns  to  the  same  situation  on  the  sun's  disc  (determined 
from  a  series  of  accurate  observations)  is  27d.  12h.  20m. ;  now  the  mean  motion 
of  the  earth  in  that  time  is  27"  7'  :  hence  360^  X  °7'  8''.  :  27d.  12h.  20m.  :  : 
SeO"*  :  25d.  14h.  4m.,  the  time  of  rotation. 

t  Sir.  I.  Newton's  Princip.  Book  iii.  Prop.  11.  &  12. 

}  Walker's  Familiar  Philosophy,  Lecture  xi.  page  516. 

§  The  semi-diameter  of  the  earth  has  been  determined  at  page  76,  in  the  note, 
to  be  3982  miles ;  and  the  distance  of  the  earth  from  the  sun  is  23882.84  semi- 
diameters  of  the  earth.  See  the  note,  page  80.  Now  the  apparent  semi-diame- 
ter mn  of  the  sun  {Plate  IV.  Fig.  3.)  is  measured  by  the  angle  mon  =  32'  2^' : 

180  — 32' 2" 

hence  the  angle  omn=the  angle  onmn=  =89^  43'  59" ;  and  on  ac- 

2 

count  of  the  distance  of  the  sun  from  the  earth,  om,  oc,  and  on-  may  be  considered 
as  equal.  Hence, 


Chap.  V. 


OP  THE  SOLAR  SYSTEM. 


141 


real  diameter  will  be  886149  miles  ;  and  as  the  magnitudes  of  all 
spherical  bodies  are  as  the  cubes*  of  their  diameters,  the  mag- 
nitude of  the  sun  will  be  I3776I3  times  that  of  the  earth ;  the 
diameter  of  the  earth  being  only  7920  miles,  the  diameter  of  the 
sun  is  above  one  hundred  and  eleven  times  the  diameter  of  the 
earth. 

II.  Of  Mercury  ^. 

Mercury  is  the  least  of  all  the  planets,  whose  magnitudes  are 
accurately  known,  and  the  nearest  to  the  sun.  The  incHnation 
of  its  axis  to  the  plane  of  its  orbit,  and  the  time  it  takes  to  re- 
volve on  its  axis,  are  unknown  ;  consequently  the  vicissitudes  of 
its  seasons,  and  the  length  of  its  day  and  night,  are  likewise  un- 
known. Mercury  is  seen  through  a  telescope  sometimes  in  the 
form  of  a  half-moon,  and  sometimes  a  little  more  or  less  than  half 
its  disc  is  seen ;  hence  it  is  inferred,  that  he  has  the  same  phases 
as  the  moon,  except  that  he  never  appears  quite  round,  because 
his  enlightened  side  is  never  turned  directly  towards  us,  unless 
when  he  is  so  near  the  sun  as  to  become  invisible,  by  reason  of 
the  splendour  of  the  sun's  rays. — The  enlightened  side  of  this 
planet  being  always  towards  the  sun,  and  his  never  appearing 
round,  are  evident  proofs  that  he  shines  not  by  his  own  light ;  for, 
if  he  did,  he  would  constantly  appear  round.  The  best  observa- 
tions of  this  planet  are  those  made  when  he  is  seen  on  the  sun's 
disc,  called  his  transit ;  for  in  his  lower  conjunction  he  sometimes 
passes  before  the  sun,  like  a  little  spot,  eclipsing  a  small  part  of 
the  sun's  body.  The  last  transit  of  mercury  was  on  the  22d  of 
November,  1822;  it  was  not  visible  at  Greenwich.  That  node 
from  which  Mercury  ascends  northward  above  the  ecliptic  is  in 
the  fifteenth  degree  of  Taurusf,  and  consequently  the  opposite  or 
descending  node  is  in  the  fifteenth  degree  of  Scorpio.  The  sun 
is  in  the  fifteenth  degree  of  Taurus  on  the  6th  of  May,  and  in  the 
fifteenth  of  Scorpio  on  the  7th  of  November;  and  when  Mer- 


Sine  omn  89o  43'  59"   9.9999953 

Is  to  23832.84  semi-diameters  :  .  .  .  .  4.3780860 

As  sine  m  o  n  32'  2''   7.9693152 

Is  to  222.5388  semi-diameters  :  .  .  .  .  2.3474059 
Now,  222.5388  X  3982=886149.5016  miles,  the  diameter  of  the  sun,  the  cube  of 
which  divided  by  the  cube  of  7964,  the  diameter  of  the  earth,  gives  1377613  times 
the  sun  is  larger  than  the  earth. 
*  EucUd  xii.  and  18th. 

t  The  place  of  Mercury's  ascending  node  for  1750  was  15o  20^  43"  in  Taurus, 
and  its  variation  in  one  hundred  years  is  1°  12'  10". — Vince's  Astronomy. 


142 


OF  THE  SOLAR  SYSTEM. 


Part  II. 


cury  comes  to  either  of  his  nodes  at  his  inferior  conjunction  (viz. 
when  he  is  between  the  earth  and  the  sun),  he  will  pass  over  the 
sun's  disc,  if  it  happen  on  or  near  the  days  above  mentioned  ;  but 
in  all  other  parts  of  his  orbit,  he  goes  either  above  or  below  the 
sun,  and  consequently  his  conjunctions  are  invisible. 

Mercury  performs  his  periodical  revolution  round  the  sun  in 
87  d.  23  h.  15  min.  43  sec. ;  his  greatest  elongation  is  28''  20', 
distance  from  the  sun  36814721*  miles  ;  the  eccentricity  of  his 
orbit  is  estimated  at  one-fifth  of  his  mean  distance  from  the  sun  ; 
his  apparent  diameter  11"  ;  hence  his  real  diameter  is  3108 


*  According  to  Laplace,  Mercury's  sidereal  period  is  87.96925S  days,  and  his 
mean  distance  from  the  sun  is  .337098,  assuming  the  earth's  distance  as  a  standard 
and  equal  to  1. 

The  distance  of  Mercury,  or  any  planet,  from  the  sun,  may  be  found  by  Kepler's 
rule.  Thus,  the  square  of  the  time  which  the  earth  takes  to  revolve  round  the  sun, 
is  to  the  cube  of  the  mean  distance  of  the  earth  from  the  sun,  as  the  square  of  the 
time  which  any  other  planet  takes  to  revolve  round  the  sun,  is  to  the  cube  of  its 
mean  distance ;  the  cube-root  of  which  will  give  the  distance  sought.  Or,  which  is 
shorter,  divide  the  square  of  the  time  in  which  any  planet  revolves  round  the  sun, 
by  the  square  of  the  time  in  which  the  earth  revolves  round  the  sun,  the  cube-root 
of  the  quotient  will  give  the  relative  distance  of  the  planet  from  the  sun.  This 
relative  distance,  multiplied  by  the  mean  distance  of  the  earth  from  the  sun,  will 
^ive  the  mean  distance  of  the  planet  from  the  sun. 

First  for  Mercury.  The  earth  revolves  round  the  sun  in  365  d.  5  h.  48  min.  48 
sec.==31 556928  sec.  the  square  of  which  is  995839704797184,  a  constant  divisor 
for  all  the  planets,  and  23882.84,  the  distance  of  the  earth  from  the  sun  in  semi- 
diameters  (see  page  80,  note)  will  be  a  constant  multiplier,  .87  d.  23  h.  15  m.  43 
sec.=7600543  sec.  the  square  of  which  is  57768253894849,  This  square  divided 
by  the  former,  gives  .0580096  nearly,  the  cube-root  of  which  is  .38710991,  the 
•distance  of  Mercury  from  the  sun,  supposing  the  distance  of  the  earth  from  the 
sua  to  be  an  unit.  .38710991  X  23882.84=9245.2841  distance  of  Mercury  from 
the  sun  in  semi-diameters  of  the  earth ;  hence  9245.2841  X  3982,  radius  of  the 
earth,=36814721  miles,  the  mean  distance  of  Mercury  from  the  sun. 

The  distance  of  the  inferior  planets  from  the  sun  may  be  found  by  their  elonga- 
tions. M.  de  la  Lande  has  calculated  that,  when  Mercury  is  in  his  aphelion,  and 
4he  earth  in  its  perigee,  the  greatest  elongation  of  Mercury  is  28°  20^ ;  but  when 
Mercury  is  in  his  perihelion,  and  the  earth  in  its  apogee,  the  greatest  elongation  is 
17°  36' ;  the  medium,  therefore,  is  22°  58'.  Hence,  in  the  triangle,  sev.  {Plate  II. 
Fig  2.)  the  angle  sev=22°  58',  the  distance  of  the  earth  from  the  sun  se=23882.84 
semi-diameters,  and  evs  is  a  right  angle. 


Hence  9318976  X  3982=37108162  miles,  the  distance  of  Mercury  from  the  sun  by 
this  method  ;  but  an  error  of  a  few  seconds  in  the  elongation  will  laak^  a  conp 
siderable  difference. 


Radius,  sine  of  90° 
Is  to  SE=23882.84  . 
As  sine  of  22^  58'  . 


10.0000000 
4.3780860 
9.5912823 
3.9693683 


Is  to  9318.976  semi-diameters 


Chap.  V. 


OF  THE  SOLAR  SYSTEM. 


143 


miles  ;*  and  his  magnitude  about  one-sixteenth  of  the  magnitude 
of  the  earth. 

Mercury  emits  a  bright  white  light ;  he  appears  a  little  after 
sun-set,  and  again  a  little  before  run-rise  ;  but,  on  account  of  his 
nearness  to  the  sun,  and  the  smallness  of  his  magnitude,  he  is  sel- 
dom seen.  The  light  and  heat  which  this  planet  receives  from 
the  sun,  is  about  seven  times  greater  than  the  light  and  heat  which 
the  earth  receives.f  The  orbit  of  Mercury  makes  an  angle  of 
seven  degrees  with  the  ecliptic,  and  he  revolves  round  the  sun 
at  the  rate  of  upwards  of  one  hundred  and  nine  thousand  miles 
per  hour.J  The  manner  in  which  the  earth  revolves  round  the 
sun  has  already  been  explained  at  page  66,  and  as  all  the  other 
planets  move  in  a  similar  manner  in  elliptical  orbits,  having  the 
sun  in  one  of  the  foci,  what  has  been  observed  respecting  the 
earth  will  be  equally  applicable  to  all  the  planets. 


Venus  is  the  brightest,  and,  to  all  appearance,  the  largest  of  all  the 
planets ;  her  light  is  distinguished  from  that  of  the  other  planets 


*  The  mean  distance  of  the  earth  from  the  sun  is  23882.84  semi-diam.,  and 
Mercury's  distance  9245.2341  semi-diam. :  the  difference  is  14637.5559  semi-diam.: 
the  distance  of  Mercury  from  the  earth ;  and,  as  the  magnitudes  of  all  bodies  vary 
inversely  as  their  distances,  we  have  by  the  rule-of-three  inverse  14637.5559  : 
11''  :  :  23882.84:  6.74179",  the  apparent  diameter  of  Mercury,  at  a  distance  from 
the  earth  equal  to  that  of  the  sun.  Now  the  mean  apparent  diameter  of  the  sun  is 
32'  2",  and  its  real  diameter  886149  miles ;  hence  32'  2"  :  886149  m. :  :  6".74179 : 
3108  miles  of  the  diameter  of  Mercury :  and,  if  the  cube  of  the  diameter  of  the  earth 
be  divided  by  the  cube  of  the  diameter  of  Mercury,  the  quotient  will  be  16.8  times 
the  magnitude  of  the  earth  exceeds  that  of  Mercury. 

The  diameter  of  Mercury  might  have  been  found  exactly  in  the  same  manner 
as  the  diameter  of  the  sun  was  found  in  the  note,  page  140,  using  11"  instead  of 
32'  2",  and  14637,5559  semi-diam.  instead  of  23882.84  semi-diam.:  the  result  of  the 
operation  in  this  case  will  be  .78061  semi-diam.  of  the  earth;  hence  .78061  X  3982 
=  3108  miles  the  diameter  of  Mercury  exactly  as  above.  It  has  been  remarked 
at  page  80,  that  the  apparent  diameters  of  the  planets  are  measured  by  a  microme- 
ter, said  to  be  invented  by  M.  Azout,  a  Frenchman ;  but  it  appears,  from  the  Philo- 
sophical Transactions,  that  it  was  invented  by  Mr.  Gascoigne,  an  Englishman. 

f  As  the  effects  of  light  and  heat  are  reciprocally  proportional  to  the  squares 
of  the  distances  from  the  centre  whence  they  are  propagated,  if  you  divide  the 
square  of  the  earth's  distance  from  the  sun,  by  the  square  of  Mercury's  distance 
from  the  sun,  the  quotient  will  show  the  comparative  heat  of  Mercury  to  that  of 
the  earth. 

X  This  is  found  in  the  same  manner  as  for  the  earth  in  page  81.  Thus,  if  j^ou 
double  the  distance  of  any  planet  from  the  sun,  then  multiply  by  355,  and  divide 


III.  Of  Venus  9. 


144 


OF  THE  SOLAR  SYSTEM. 


Part  II. 


by  its  brilliancy  and  whiteness,  which  are  so  considerable  that, 
in  a  dusky  place,  she  causes  an  object  to  cast  a  sensible  shadow. 
Venus,  when  viewed  through  a  telescope,  appears  to  have  all  the 
phases  of  the  moon,  from  the  crescent  to  the  enlightened  hemis- 
phere, though  she  is  seldom  seen  perfectly  round.  Her  illumin- 
ated part  is  constantly  turned  towards  the  sun  ;  hence,  the  con- 
vex part  of  her  cresent  is  turned  towards  the  east  when  she  is  a 
morning  star,  and  towards  the  west  when  she  is  an  evening  star ; 
for  when  Venus  is  west  of  the  sun,  as  seen  from  the  earth,  that 
is,  when  her  longitude  is  less  than  the  sun's  longitude,  she  rises 
before  him  in  the  morning,  and  is  then  called  a  morning  star ;  but 
when  she  is  east  of  the  sun,  viz.  when  her  longitude  is  greater 
than  the  sun's  longitude,  she  shines  in  the  evening  after  the  sun 
sets,  and  is  then  called  an  evening  star. 

Venus  is  a  morning  star,  or  appears  west  of  the  sun  for  about 
290  days,  and  she  is  an  evening  star,  or  appears  east  of  the  sun 
for  nearly  the  same  length  of  time,  though  she  performs  her  whole 
revolution  round  the  sun  in  224  days  16  hours  49  minutes  10 
seconds.  A  very  natural  question  here  may  be  asked,  viz. 
Why  Venus  appears  a  longer  time  to  the  eastward  or  westward 
of  the  sun  than  the  whole  time  of  her  entire  revolution  round  him? 
This  is  easily  answered,  by  considering  that,  while  Venus  is  going 
round  the  sun,  the  earth  is  going  round  him  the  same  way,  though 
slower  than  Venus,  and  therefore  the  relative  motion  of  Venus 
is  slower  than  her  absolute  motion. 

Sometimes  Venus  is  seen  on  the  disc  of  the  sun  in  the  form  of 
a  dark  round  spot.  These  appearances  happen  but  seldom,  viz. 
they  can  happen  only  when  Venus  is  between  the  earth  and  the 
sun,  and  when  the  earth  is  nearly  in  a  line  with  one  of  the  nodes 
of  Venus.*  The  last  transit  of  Venus  was  in  1769,  and  the  two 
next  transits,  in  succession,  will  fall  on  the  8th  of  December, 
1874,  and  on  the  7th  of  June,  2004.  The  time  which  this  planet 
takes  to  revolve  on  its  axis,  and  the  inclination  of  its  axis  to  the 
plane  of  its  orbit,  have  been  given  by  different  astronomers; 


the  last  product  by  113,  you  obtain  the  circumference  of  the  planet's  orbit  in  miles. 
This  circumference,  divided  by  the  number  of  hours  in  the  planet's  year,  will  give 
the  number  of  miles  per  hour  which  that  planet  travels  round  the  sun  :  a  general 
rule  for  all  the  planets.  Hence, 

The  circumference  of  Mercury's  orbit  will  be  found  to  be  231313733.717  miles  ; 
then  87d.  23h.  15'  43'' :  231313733.717  miles  :  :  1  h.  :  109561  miles  Mercury  travels 
per  hour. 

*  The  place  of  the  ascending  node  of  Venus  for  1750  was  14°  26'  18"  in  Gemini, 
and  its  variation  in  100  years  is  51'  40",    Vince^s  Astronomy. 


Chap.  V. 


OF  THE  SOLAR  SYSTEM. 


145 


but  Dr.  Herschel,  from  a  long  series  of  observations  on  this 
planet,  published  in  the  Philosophical  Transactions  for  1793,  con- 
cludes, that  the  time  of  this  planet's  rotation  on  its  axis  is  uncer- 
tain and  that  the  position  of  its  axis  is  equally  uncertain ;  that  its 
atmosphere  is  very  considerable  ;  that  it  has  probably  inequalities 
on  its  surface,  yet  he  cannot  discover  any  mountains.  The  ap- 
parent diameter  of  Venus  is  stated  to  be  58''  .79;  the  eccentri- 
city of  her  orbit  473100  miles  ;*  her  greatest  elongation  47°  48' ; 
her  revolution  round  the  sun  is  performed  in  224  d.  16  h.  49  m. 
10  sec.jf  as  before  stated  ;  and,  if  her  apparent  diameter  be  taken 
as  above,  her  true  diameter  will  be  7498  miles,J  and  her  magni- 
tude something  less  than  that  of  the  earth  ;  likewise  her  distance 
from  the  sun  will  be  found  to  be  68791752  miles. 

The  light  and  heat  which  this  planet  receives  from  the  sun, 
are  about  double  to  what  the  earth§  receives.  The  orbit  of  Ve- 
nus makes  an  angle  of  3°  23'  35''  with  the  ecliptic,  and  she  re- 
volves round  the  sun  at  the  rate  of  upwards  of  eighty  thousand 


+  For,  according  to  M.  de  la  Lande,  if  the  mean  distance  of  the  earth  be  100000, 
the  eccentricity  of  Venus  will  be  498;  hence,  when  the  distance  .is  95  millions  of 
miles,  the  eccentricity  will  be  473100  miles. 

t  The  seconds  in  this  time=19414150,  the  square  of  which  is  376909220222500, 
this  divided  by  995839704797184  (see  the  note,  page  142.)  gives  .3784838,  &c.  the 
cube  root  of  which  is  .723351 1 ;  this,  multipHed  by  23882.84,  produces  17275.678585 
semi-diam.  which,  multiplied  by  3982=68791752  miles,  the  distance  of  Venus  from 
the  sun. 

According  to  Laplace,  the  sidereal  revolution  of  Venus  is  224.700824  days,  and 
her  mean  distance  from  the  sun  is  .723332. 

M.  de  la  Lande  has  found  the  greatest  elongations  of  Venus  to  be  47°  48'  and 
44°  57'  when  in  similar  situations  to  Mercury,  mentioned  in  the  note,  page  143. ; 
the  medium  is  46^  22'  30",  using  this  angle  and  the  very  same  calculation  as  in  the 
note  page  143,  the  distance  of  Venus  from  the  sun  will  be  found  =17288.09  semi- 
diameters  of  the  earth;  hence  the  distance  will  be  had  =  68841 174  miles  aston- 
ishingly near  the  distance  found  by  Kepler's  rule,  considering  the  great  difference 
in  the  principles  of  calculation,  and  a  strong  proof  of  the  truth  of  the  Copernican 
system. 

X  Here,  (as  in  the  note,  page  143,)  23882.84—17275.678585  =  6607.16145  semi- 
diara.  distance  of  Venus  from  the  earth;  hence,  inversely  6607.16145 :  58" .79; 
;  23882.84:  16"  .26419,  and  32' 2" :  886149:  :16'.26419:  7498  miles,  the  diameter 
of  Venus.  Or,  by  trigonometry,  using  the  angle  58".79,  and  distance  6607.16145, 
the  result  is  1 . 883 1 4 ;  X  3982  =  7498  miles. 

§  These  are  found  by  dividing  the  square  of  the  earth's  distance  from  the  sun  by 
the  square  of  the  distance  of  Venus  from  the  sun. 

The  earth's  distance  from  the  sun  is  95000000  miles,  the  square  of  which  is 
9025000000000000,  the  distance  of  Venus  from  the  sun  is  68791752  miles,  the 
square  of  which  is  4732305143229504 ;  the  former  square  divided  by  the  latter 
giveB  1.907  for  the  quotient. 


146 


OF  THE   SOLAR  SYSTEM. 


Part  IL 


miles  per  hour.^  This  planet,  like  Mercury,  never  departs  from 
the  Sim  ;  she  is  only  visible  a  few  hours  in  the  morning  before  the 
sun  rises,  or  in  the  evening  after  he  sets ;  an  evident  proof  that 
the  orbits  of  these  planets  are  contained  within  the  orbit  of  the 
earth,  otherwise  they  would  be  seen  in  opposition  to  the  sun,  or 
above  the  horizon  at  midnight. 

IV.  Of  the  Earth  ©,  and  its  Satellite  the  Moon©. 

The  figure  and  magnitude  of  the  earth  have  been  already  ex- 
plained in  Chapter  III.  Part  J. ;  and  its  diurnal  and  annual  rev- 
olution round  the  sun,  distance  from  the  sun,  seasons  of  the  year, 
&LC.  have  been  shown  in  Chapter  IV.;  as  it  would  appear  super- 
fluous to  repeat  those  particulars  here,  this  chapter  is  confined 
entirely  to  the  moon. 

The  moon  being  the  nearest  celestial  body  to  the  earth,  and, 
next  to  the  sun,  the  most  resplendent  in  appearance,  has  excited 
the  attention  of  astronomers  in  all  ages.  The  Hebrews,  the 
Greeks,  the  Romans,  and,  in  general,  all  the  ancients,  used  to  as- 
semble at  the  time  of  new,  or  full  moon,  to  discharge  the  duties 
of  piety  and  gratitude  for  its  manifold  uses.  The  day  being  meas- 
ured by  observing  the  time  which  the  sun  took  in  apparently 
moving  from  any  meridian  to  the  same  again,  so  the  month  was 
measured  by  the  number  of  days  elapsed  from  new  moon  to  new 
moon ;  this  month  was  supposed  to  be  completed  in  thirty  days;-f- 
and  when  the  motion  of  the  moon  came  to  be  compared  with, 
and  adjusted  to,  the  apparent  motion  of  the  sun,  twelve  of  these 
months  were  thought  to  correspond  exactly  with  the  sun's  annual 
course.  The  lunar  month  is  of  two  sorts,  periodical  and  synod- 
ical.  A  periodical  month  is  the  time  in  which  the  moon  finishes 
her  course  round  the  earth,  and  consists  of  27  days  7  hours  43 


*  By  the  process  mentioned  in  the  note,  page  143.,  the  circumference  of  the 
orbit  of  Venus  will  be  found  to  be  432231362.123  miles;  then,  as  224d.  16 h. 
49  ra.  10  sec. :  432231362.123  miles :  :  1  h. :  80149  miles  Venus  travels  per  hour. 

I  The  Rev.  M.  Costard,  in  his  History  of  Astronomy,  supposes  that  the  oldest 
measure  of  time  (taken  from  the  revolutions  of  the  heavenly  bodies)  was  a  month  ; 
and,  after  the  length  of  the  year  was  discovered,  the  echptic,  and  all  other  circles, 
were  divided  into  360  equal  parts,  called  degrees,  because  30  d.  X  12=  360  days, 
the  length  of  the  year. — Hist,  of  Astr.  p.  44.  In  an  account  of  the  Pelew  Islands, 
we  are  told  that  the  inhabitants  reckoned  their  time  by  months,  and  not  by  years  ; 
for,  when  the  king  entrusted  his  son  to  the  care  of  Captain  Wilson,  he  inqured 
how  many  moons  would  elapse  before  he  might  expect  the  return  of  his  son.  The 
inhabitants  of  these  islands  were  totally  ignorant  of  the  arts  and  sciences. 


Chap,  V. 


OF  THE  SOLAR  SYSTEM. 


147 


minutes  5  seconds  and  a  synodical  month  is  the  time  elapsed 
from  new  moon  to  new  moon,  and  consists  of  29  days  12  hours  44 
minutes  3  seconds.  The  synodical  month  was  probably  the  only 
one  observed  in  the  infancy  of  astronomy. 

The  orbit  of  the  moon  is  nearly  elliptical,  having  the  earth  in 
one  of  its  foci ;  but  the  eccentricity  of  this  ellipsis  is  variable, 
being  the  greatest  when  the  line  of  the  apsides  is  in  the  syzygies, 
for  then  the  transverse  axis  of  the  moon's  orbit  is  lengthened ; 
and  the  least  when  the  transverse  axis  is  in  the  quadratures,  for 
then  the  conjugate  axis  is  lengthened,  and  consequently  the  orbit 
approaches  nearer  to  a  circle.  The  moon  in  her  revolution 
round  the  earth  would  always  describe  the  same  ellipsis,  were 
that  revolution  undisturbed  by  the  action  of  the  sun ;  the  princi- 
pal axis  of  her  orbit  would  remain  at  rest,  and  be  always  of  the 
same  quantity ;  her  periodic  times  would  all  be  equal,  and  the 
inclination  of  her  orbit  to  the  ecliptic  and  the  place  of  her  nodes 
would  be  invariable ;  but  her  motions  being  disturbed  by  the  ac- 
tion of  the  sun,  they  become  subject  to  so  many  irregularities, 
that  to  calculate  the  moon's  place  truly,  and  to  establish  the  ele- 
ments of  her  theory,  are  almost  insuperable  difficulties. 

The  orbit  of  the  moon  is  inclined  to  the  ecliptic  in  an  angle, 
which  is  variable  from  5^  to  5*^  18',  consequently  it  is  inclined  in 
an  angle  of  5°  9'  at  a  medium.  The  motion  of  the  moon's  nodes, 
or  places  where  her  orbit  crosses  the  orbit  of  the  earth,  is  west- 
ward, or  contrary  to  the  order  of  the  signs :  this  motion  is  like- 
wise variable,  but  by  comparing  together  a  great  number  of  dis- 
tant observations,  the  mean  annual  retrograde  motion  is  found  to 
be  about  19°  19'  44'^,  so  that  the  nodes  make  a  complete  retro- 
grade revolution  from  any  point  of  the  ecliptic  to  the  same  again 
in  about  18  years  228  days  9  hours.  The  axis  of  the  moon  is 
almost  perpendicular  to  the  plane  of  the  ecliptic,  the  angle  being 
88*^  17',  consequently  she  has  little  or  no  diversity  of  seasons. 
The  moon  turns  round  her  axis,  from  the  sun  to  the  sun  again, 
in  29  days  12  hours  44  minutes  3  seconds,  which  is  exactly  the 
time  that  she  takes  to  go  round  her  orbit  from  new  moon  to  new 
moon,  she  therefore  has  constantly  the  same  side  turned  towards 
the  earth.  This,  however,  is  subject  to  a  small  variation,  called 
the  librationf  of  the  moon,  so  that  she  sometimes  turns  a  little 


*  Periodical  revolution  27.3215S2  days,  synodical  29.530538.    M.  Laplace. 

I  A  lunar  globe  was  published  a  few  years  ago  by  Mr.  Russel,  which  shows  not 
only  the  libration  of  the  moon  in  the  most  perfect  maimer,  but  is  a  complete  picture 
of  the  mountains,  pits,  and  sh'ades,  on  her  surface. 


/ 


148 


OF  THE  SOLAR  SYSTEM. 


Part  XL 


more  of  the  one  side  of  her  face  towards  the  earth,  and  some- 
times a  little  more  of  the  other,  arising  from  her  uniform  motion 
on  her  axis  and  unequal  motion  in  her  orbit :  this  is  called  her 
libration  in  longitude.  The  moon  hkewise  appears  to  have  a 
kind  of  vacillating  motion,  w^hich  presents  to  our  view  sometimes 
more  and  sometimes  less  of  the  spots  on  her  surface  towards  each 
pole  ;  this  arises  from  the  axis  of  the  moon  making  an  angle  of 
about  P  43'  with  a  perpendicular  to  the  plane  of  the  echptic; 
and  as  this  axis  maintains  its  parallelism  during  the  moon's  revo- 
lution round  the  earth,  it  must  necessarily  change  its  situation  to 
an  observer  on  the  earth ;  this  is  called  the  moon's  libration  in 
latitude. 

While  the  moon  revolves  round  the  earth  in  an  elliptical  or- 
bit, she  likewise  accompanies  the  earth  in  its  elliptical  orbit  round 
the  sun  ;  by  this  compound  motion  her  path  is  every  where  con- 
cave towards  the  sun.* 

The  moon,  like  the  planets,  is  an  opaque  body,  and  shines  en- 
tirely by  the  light  received  from  the  sun,  a  portion  of  which  is 
reflected  to  the  earth.  As  the  sun  can  only  enlighten  one-half  of 
a  spherical  surface  at  once,  it  follows  that  according  to  the  situa- 
tion of  an  observer,  with  respect  to  the  illuminated  part  of  the 
moon,  he  w^ill  see  more  or  less  of  the  light  reflected  from  her  sur- 
face. At  the  conjunction,  or  time  of  new  moon,  the  moon  is  be- 
tween the  earth  and  the  sun,  and  consequently  that  side  of  the 
moon  which  is  never  seen  from  the  earth  is  enlightened  by  the 
sun ;  and  that  side  which  is  constantly  turned  towards  the  earth 
is  wholly  in  darkness.f  Now,  as  the  mean  motion  of  the  moon 
in  her  orbit  exceeds  the  apparent  motion  of  the  sun  by  about  12° 
ir  in  a  day, J  it  follows  that,  about  four  days  after  the  new  moon, 
she  will  be  seen  in  the  evening  a  little  to  the  east  of  the  sun,  af- 
ter he  has  descended  below  the  western  part  of  the  horizon.  A 
spectator  will  see  the  convex  part  of  the  moon  towards  the  west, 
and  the  horns  or  cusps  towards  the  east :  or  if  the  observer  live  in 
north  latitude,  as  he  looks  at  the  moon  the  horns  will  appear  to 
the  left  hand ;  for  if  the  line  joining  the  cusps  of  the  moon  be 
bisected  by  a  perpendicular  passing  through  the  enlightened  part 


*  See  M.  Maclaurin's  account  of  Sir  Isaac  Newton's  discoveries,  book  iv.  chap.  5 ; 
Rowe's  Fluxions,  second  edition,  page  225. ;  Ferguson's  Astronomy,  octavo  edi- 
tion, article  226.;  or,  a  Treatise  on  Astrononny,  by  Dr.  Olinthus  Gregory,  article  458. 

t  Except  the  light  which  is  reflected  upon  it  from  the  earth,  which  we  cannot 
perceive. 

X  See  the  note,  page  91.  • 


Cluip,  V. 


OF  THE  SOLAR  SYSTEM. 


149 


of  the  moon,  that  perpendicular  will  point  directly  to  the  sun. 
As  the  moon  continues  her  motion  eastward,  a  greater  portion 
of  her  surface  towards  the  earth  becomes  enlightened  ;  and  when 
she  is  90  degrees  eastward  of  the  sun,  which  will  happen  about 
7^  days  from  the  time  of  new  moon,  she  will  come  to  the  me- 
ridian about  six  o'clock  in  the  evening,  having  the  appearance  of 
a  bright  semi-circle  ;  advancing  still  to  the  eastward,  she  becomes 
more  enlightened  towards  the  earth,  and  at  the  end  of  about  14f 
days,  she  will  come  the  meridian  at  midnight,  being  diametrically 
opposite  to  the  sun  ;  and  consequently  she  appears  a  complete  cir- 
cle, or  it  is  said  to  hQ  full  moon.  The  earth  is  now  between  the 
sun  and  the  moon,  and  that  half  of  her  surface  which  is  constantly 
turned  towards  the  earth  is  wholly  illuminated  by  the  direct  rays 
of  the  sun ;  whilst  that  half  of  her  surface,  which  is  never  seen 
from  the  earth  is  involved  in  darkness.  The  moon  continuing 
her  progress  eastward,  she  becomes  deficient  on  her  western 
edge,  and  about  1^  days  from  the  full  moon  she  is  again  within 
90  degrees  of  the  sun,  and  appears  a  semi-circle  with  the  convex 
side  turned  towards  the  sun :  moving  on  still  eastward,  the  de- 
ficiency on  her  western  edge  becomes  greater,  and  she  appears  a 
crescent,  with  the  convex  side  turned  towards  the  east,  and  her 
cusps  or  horns  turned  towards  the  west :  and  about  14^  days 
from  the  full  moon  she  has  again  overtaken  the  sun,  this  period 
being  performed  in  29  days  12  hours  44  minutes  3  seconds,  as 
has  been  observed  before.  Hence,  from  the  new  moon  to  the 
full  moon,  the  phases  are  horned,  half -moon,  and  gibbous ;  and  as 
the  convex  or  well-defined  side  of  the  moon  is  always  turned  to- 
wards the  sun,  the  horns  or  irregular  side  will  appear  to  the  east, 
or  towards  the  left  hand  of  a  spectator  in  north  latitude.  From 
the  full  moon  to  the  change,  the  phases  are  gibbous,  half  moon, 
and  horned;  the  convex  or  well-defined  side  of  her  face  will  ap- 
pear to  the  east,  and  her  horns  or  irregular  side  towards  the  west, 
or  to  the  right  hand  of  a  spectator. 

As  the  full  moons  always  happen  when  the  moon  is  directly 
opposite  to  the  sun,  all  the  full  moons,  in  our  winter,  happen 
when  the  moon  is  on  the  north  side  of  the  equinoctial.  The 
moon,  while  she  passes  from  Aries  to  Libra,  will  be  visible  at 
the  north  pole,  and  invisible  during  her  progress  from  Libra  to 
Aries ;  consequently,  at  the  north  pole,  there  is  a  fortnight's 
moonlight  and  a  fortnight's  darkness  by  turns.  The  same  phenom- 
ena will  happen  at  the  south  pole  during  the  sun's  absence  in  our 
summer.  Ijf  the  earth,  the  moon,  and  the  sun  were  all  in  the  same 
plane,  there  would  be  an  eclipse  of  the  sun  at  every  new  moon, 
(for  then  the  moon  is  between  the  earth  and  the  sun,)  and  there 


150 


OF  THE   SOLAR  SYSTEM. 


Part  II. 


would  be  an  eclipse  of  the  moon  at  every  full  moon,  at  which 
time  the  earth  is  between  the  sun  and  the  moon.  But  as  the  or- 
bit of  the  moon  crosses  the  orbit  of  the  earth  or  the  ecliptic  in 
two  opposite  points  called  the  nodes,  it  is  evident  that  the  moon 
is  never  in  the  ecliptic  except  when  she  is  in  one  of  these  nodes ; 
an  eclipse,  therefore,  can  never  happen  unless  the  moon  be  in  or 
near  one  of  these  nodes  ;  at  all  other  times  she  is  either  above  or 
below  the  orbit  of  the  earth ;  and  though  the  moon  crosses  each 
of  these  nodes  every  month,  yet  if  there  should  not  be  a  new  or 
full  moon,  at  or  near  that  time,  there  will  be  no  eclipse.  {See 
more  of  this  subject  in  a  succeeding  chapter.)  The  influence  of 
the  moon  upon  the  waters  of  the  ocean  has  already  been  explain- 
ed ;  and  the  nature  of  the  harvest-moon  will  be  shown  amongst 
the  problems  on  the  globes. 

The  moon's  greatest  horizontal  parallax  is  6 T  32'',  the  least 
54'  4/',  consequently  the  mean  horizontal  parallax  is  57'  48"*  ; 
and  her  mean  distance  from  the  earth  236847  miles.-|-  The  ap- 
parent diameter  of  the  moon  is  variable  according  to  her  distance 
from  the  earth ;  her  mean  apparent  diameter  is  stated  to  be  31' 
7"J  ;  hence  her  real  diameter  is  2144  mi]es§,  and  her  magnitude 
about  of  the  magnitude  of  the  earth.  The  moon  performs  her 
revolutions  round  the  earth  in  27  days  7  hours  43  minuts  5  sec- 
onds, and  has  been  observed  before,  consequently  she  travels  at  the 


*  Dr.  Hutton's  Mathematical  Diet,  word  Parallax. 

f  As  in  the  note,  page  80. 

Sine  of  angle  pso  57M8'^  ....  8.2256335 
Is  to  semi-diameter  of  the  earth  po  -  0.0000000 
As  to  radius,  sine  of  90  =sine  ops  -  10,0000000 
Is  to  59.47938  semi-diameters,  -  -  1.7743665 
Hence  59.47938  X  3882=236846.89  miles,  distance  of  the  moon  from  the  earth. 

j  Fince's  Astronomy.    PTooc^/ioiise's  Astronomy,  page  314. 

§  As  in  the  preceding  notes  say,  inversely,  59.47938  semi-diam.  :  31' 7''' :  : 
23382.84  sem.  :  4". 6497,  the  apparent  diameter  of  the  moon  at  a  distance  from 
the  earth  equal  to  that  of  the  sun;  hence  32'  2'':  886149':  4''.6497  :  2143.8 
miles  the  diameter  of  the  moon.  Or,  by  trigonometry,  the  angle  m  o  n,  {Plate 
IV.  Fig.  3.)=31'  T',  hence 
180  —31'  T' 

0  m  n=  =89 '  59'  44"  26^-"'. 

2 

Sine  of  89°  59'  44",  &c.  =  (sine  of  90  nearly  -    -    -    -  10.0000000 

Is  to  59.47938  semi-diameters   1.7743665 

As  sine  31' 7"   7.9567310 

Is  to  .53839  semi-diameters  of  the  earth   1.7310975 

And  to  .53839  X  3982=2143.86,  &c.  miles  the  diameter  of  the  moon  :  See  the 
notes,  page  143.  If  the  cube  of  the  earth's  diameter  be  divided  by  the  cube  of  the 
moon's  diameter,  the  quotient  will  be  51.2  ;  hence  the  magnitude  of  the  earth  is 
upwards  of  50  times  that  of  the  moon. 


Chap.  V. 


OF  THE  SOLAR  SYSTEM. 


151 


rate  of  2270^  miles  per  hour  round  the  earth,  besides  attending 
the  earth  in  its  annual  journey  round  the  sun. 

The  surface  of  the  moon  is  greatly  diversified  with  inequalities, 
which  through  a  telescope  have  the  appearance  of  hills  and  val- 
lies.  Astronomers  have  drawn  the  face  of  the  moon  as  viewed 
through  a  telescope,  distinguishing  the  dark  and  shining  parts  by 
their  proper  shades  and  figures.  Each  of  the  spots  on  the  moon 
has  been  marked  by  a  numerical  figure,  serving  as  a  reference  to 
the  proper  name  of  the  particlar  spot  which  it  represents ;  as,  >1< 
Herschei's  volcano;  l,Grimaldi;  2,  Galileo,  &c. ;  so  that  the 
several  spots  are  named  from  the  most  noted  astronomers,  philos- 
ophers, and  mathematicians.  The  best  and  most  complete  pic- 
ture of  the  moon  is  that  drawn  on  Mr.  Russel's  lunar  globe. 

Dr.  Herschel  informs  us  that,  on  the  19th  of  April,  1787,  he 
discovered  three  volcanoes  in  the  dark  part  of  the  moon  ;  two  of 
them  appeared  nearly  extinct,  the  "third  exhibited  an  actual  erup- 
tion of  fire,  or  luminous  matter.  On  the  subsequent  night  it  ap- 
peared to  burn  with  greater  violence,  and  might  be  computed  to 
be  about  three  miles  in  diameter.  The  eruption  resembled  a 
piece  of  burning  charcoal,  covered  with  a  thin  coat  of  white  ashes  ; 
all  the  adjacent  parts  of  the  volcanic  mountain  were  faintly  illu- 
minated by  the  eruption,  and  were  gradually  more  obscure  at  a 
greater  distance  from  the  crater.  That  the  surface  of  the  moon 
is  indented  with  mountains  and  caverns,  is  evident  from  the  ir- 
regularity of  that  part  of  her  surface  which  is  turned  from  the 
sun  :  for,  if  there  were  no  parts  of  the  moon  higher  than  the  rest, 
the  light  and  dark  spots  of  her  disc  at  the  time  of  the  quadratures 
would  be  terminated  by  a  perfectly  straight  line  ;  and  at  all  other 
times  the  termination  would  be  an  elliptical  line,  convex  towards 
the  enlightened  part  of  the  moon  in  the  first  and  fourth  quarters, 
and  concave  in  the  second  and  third  :  but  instead  of  these  lines 
being  regular  and  well  defined  when  the  moon  is  viewed  through 
a  telescope,  they  appear  notched  and  broken  in  innumerable  pla- 
ces. It  is  rather  singular  that  the  edge  of  the  moon,  which  is  al- 
ways turned  towards  the  sun,  is  regular  and  well  defined,  and  at 
the  time  of  full  moon  no  notches  or  indented  parts  are  seen  on 
her  surface.  In  all  situations  of  the  moon,  the  elevated  parts  are 
constantly  found  to  cast  a  triangular  shadow  with  its  vertex  turned 


*  For,  by  the  note,  page  143,  113  :  355  :  :  236S46.9  X  2  :  1488153.09  miles  cir- 
cumference of  the  moon's  orbit;  then  27  d.  7h.  43  m.  5  sec. :  1488153.09  m.  :  :  1  h. 
:  2269.5  miles. 


152 


OP  THE  SOLAR  SYSTEM. 


Part  IL 


from  the  sun  ;  and,  on  the  contrary,  the  cavities  are  always  dark 
on  the  side  next  the  sun,  and  illuminated  on  the  opposite  side  ; 
these  appearances  are  exactly  conformable  to  what  we  observe 
of  hills  and  valleys  on  the  earth  :  and  even  in  the  dark  part  of  the 
moon's  disc,  near  the  borders  of  the  lucid  surface,  some  minute 
specks  have  been  seen,  apparently  enlightened  by  the  sun's  rays  :  * 
these  shining  spots  are  supposed  to  be  the  summits  of  high  moun- 
tains*, which  are  illuminated  by  the  sun,  while  the  adjacent  val- 
leys nearer  the  enlightened  part  of  the  moon  are  entirely  dark. 

Whether  the  moon  has  an  atmosphere  or  not,  is  a  question 
that  has  long  been  controverted  by  various  astronomers :  some 
endeavour  to  prove,  that  the  moon  has  neither  an  atmosphere, 
seas,  nor  lakes  ;  while  others  contend  that  she  has  all  these  in 
common  with  our  earth,  though  her  atmosphere  is  not  so  dense 
as  ours.  It  cannot  be  expected  in  an  introductory  treatise,  where 
general  received  truths  only  ought  to  be  admitted,  that  we  should 
enter  into  the  discussion  of  a  controverted  question  ;  however, 
it  may  be  proper  to  inform  the  student,  that  the  advocates  for  an 
atmosphere,  if  we  may  be  allowed  to  reason  from  analogy,  have 


*  Supposing  this  to  be  the  fact,  astronomers  have  determined  the  height  of  some 
of  the  lunar  mountains.  The  method  made  use  of  by  Riccioli  (though  it  gives  the 
true  result  only  at  the  time  of  the  qadratures)  is  here  explained,  because  it  is  much 
more  simple  than  the  general  method  given  by  Dr.  Herschel  in  the  Philosophical 
Transactions  for  J  780.  Let  adb  {Plate  IV.  Fig.  7.)  be  the  disc  or  face  of  the  moon 
at  the  time  of  the  quadratures,  acb  the  boundary  of  light  and  darkness ;  mo  a  moun- 
tain in  the  dark  part,  the  summit  m  of  which  is  just  beginning  to  be  enlightened,  by 
a  ray  of  hght  sam  from  the  sun.  Now,  by  means  of  a  micrometer,  the  ratio  of  ma 
to  AB  may  be  determined ;  and  as  ac  is  the  half  of  ab,  and  mac  a  right  angled  trian- 
gle by  Euclid  1  and  47th  \/ac^-}-am^  =cm,  from  which  take  co  =ac,  and  the  re- 
mainder MO,  is  the  height  of  the  mountain.  Riccioh  observed  the  illuminated  part 
of  the  mountain  St.  Catherine,  on  the  fourth  day  after  the  new  moon,  to  be  distant 
from  the  illuminated  part  of  the  moon  about  1-sixteenth  part  of  the  moon's  diame- 
ter, viz.  MA  =  1-sixteenth  of  ab,  or=  1-eighth  of  ac  ;  now,  if  we  take  the  moon's  di- 
ameter 2144  miles,  as  we  have  before  determined,  the  height  of  this  mountain  will 
be  8  _3_  miles !  Galileo  makes  ma  =  l-20th  of  ab  ;  and  Hevehus  makes  ma  =  1- 
26th  of  AB ;  the  former  of  these  will  give  the  height  of  the  mountain  5_3_  miles,  and 
the  latter  3_1_  miles.  Dr.  Herschel  thinks,  "  that  the  hights  of  the  lunar  moun- 
tains are  in  general  greatly  over-rated,  and  that  the  generality  of  them  do  not  ex- 
ceed half  a  mile  in  their  perpendicular  elevation."  On  the  contrary,  M.  Schroeter, 
a  learned  astronomer  of  Lihenthal,  in  the  duchy  of  Bremen,  says,  that  there  are 
mountains  in  the  moon  much  higher  than  any  on  the  earth,  and  mentions  one  above 
a  thousand  toises  higher  than  Chimboraco  in  South  America.  The  same  author 
has  lately  published  a  new  work  on  the  heights  of  the  mountains  of  Venus,  some  of 
which  he  makes  upwards  of  twenty-three  thousand  toises  in  height,  which  is  above 
seven  times  the  height  of  Chimboraco  ! 


Chap,  V. 


OF  THE  SOLAR  SYSTEM. 


153 


the  advantage  over  those  who  contend  that  there  is  none.  It  is 
admitted  on  all  hands,  that  the  moon  has  mountains  and  valleys, 
like  the  earth,  and  appears  nearly  the  same  with  respect  to  shape 
and  the  nature  of  her  motions.  May  we  not  then  fairly  infer 
that  she  is  similar  to  the  earth  in  other  respects  ? 

V.  Of  Mars 

Mars  appears  of  a  dusky  red  colour,  and  though  he  is  some- 
times apparently  as  large  as  Venus,  he  never  shines  with  so  bril- 
liant a  light.  From  the  dulness  and  ruddy  appearance  of  this 
planet,  it  is  conjectured  that  he  is  encompassed  with  a  thick  cloudy 
atmosphere,  through  which  the  red  rays  of  light  penetrate  more 
easily  than  the  other  rays.  This  being  the  first  planet  without 
the  orbit  of  the  earth,  he  exhibits  to  the  spectator  different  ap- 
pearances to  Mercury  and  Venus.  He  is  sometimes  in  conjunc- 
tion with  the  sun,  like  Mercury  and  Venus,  but  w^as  never  known 
to  transit  the  sun's  disc.  Sometimes  he  is  directly  opposite  to 
the  sun,  that  is,  he  comes  to  the  meredian  at  midnight,  or  rises 
when  the  sun  sets,  and  sets  when  the  sun  rises  ;  at  this  time  he 
shines  with  the  greatest  lustre,  being  nearest  to  the  earth.  Mars, 
when  viewed  through  a  telescope,  appears  sometimes  full  and 
round,  at  others  gibbous,  but  never  horned.  The  foregoing  ap- 
pearances clearly  show,  that  Mars  moves  in  an  orbit  more  distant 
from  the  sun  than  that  of  the  earth.  The  apparent  motion  of 
this  planet,  like  that  of  Mercury  and  Venus,  is  sometimes  direct, 
or  from  east  to  west ;  at  others  retrograde,  or  from  west  to  east ; 
and  sometimes  he  appears  stationary.  Sometimes  he  rises  before 
the  sun,  and  is  seen  in  the  morning ;  at  others  he  sets  after  the 
sun,  and  of  course  is  seen  in  the  evening.  Mars  revolves  on  its 
axis  in  24  hours  39  minutes  22  seconds  ;  and  its  polar  diameter 
is  to  its  equatorial  diameter  as  15  to  16,  according  to  Dr.  Her- 
schel ;  but  Dr.  Maskelyne,  who  carefully  observed  this  planet  at 
the  time  of  opposition,  could  perceive  no  difference  between  its 
axes.  The  inclination  of  the  orbit  of  Mars  to  the  plane  of  the 
ecliptic  is  1°  51' ;  the  place  of  his  ascending  node  about  18°  in 
Taurus,*  his  horizontal  parallax  is  said  to  be  23".6  ;  he  performs 
his  revolution  round  the  sun  in  1  year  321  days  23  hours  15  min- 
utes 44  seconds ;  and  his  apparent  semi-diameter,  at  his  nearest 


*  The  longitude  of  the  ascending  node  of  Mars  for  the  beginning  of  the  year 
1750  was  17-  38'  38"  in  Taurus,  and  its  variation  in  100  years  is  46'  AQf'.-^Vince's 
Astronomy. 

20 


154 


OF  THE  SOLAR  SYSTEM. 


Part  11. 


distance  from  the  earth,  is  2b" ;  consequently  his  mean  distance 
from  the  sun  is  144907630*  miles ;  his  diameter  4218  miles  ; 
and  his  magnitude  a  little  more  than  ith  of  that  of  the  earth.f 
This  planet  travels  round  the  sun  at  the  rate  of  55323  miles  per 
hourj  ;  and  the  parallax  of  the  earth's  annual  orbit,  as  seen  from 
Mars,  is  about  41  degrees.  As  the  distances  of  the  interior 
planets  from  the  sun  are  found  by  their  elongations,  so  the  dis- 
tances of  the  exterior  planets  may  be  found  by  the  parallax  of 
the  earth's  annual  orbit. § 

VI.  Of  Vesta 

This  planet  was  discovered  by  Dr.  Olhers,  of  Bremen,  on  the 


*  For,  686  days  23  hours  15  min.  44  sec.=59354144  seconds,  the  square  of 
which  is  3522914409872736,  this  divided  by  995839704797184  the  seconds  in  a 
year  (see  the  note,  page  142),  gives  3.537632,  the  cube-root  of  which  is  1.523716, 
the  relative  distance  of  Mars  from  the  sun.  Hence  1.5237186  X  23882.84  = 
36390.6654  distance  of  Mars  from  the  sun  in  semi-diameters  of  the  earth,  and 
36390.6654  X  3982=144907629.6  miles,  the  mean  distance  of  Mars  from  the  sun. 
Now,  if  the  horizontal  parallax  of  Mars  at  the  time  of  opposition  be  23"  .6,  as 
stated  by  M.  de  laCaille,  we  have  (see  Plate  IV.  Fig.  6.) 

Sine  Pso=sine  23'^  .6    6.0583927 

Is  to  P0=1  semi-diameter   0.0000000 

As  radius  sine  of  90'  10.0000000 

Is  to  SG=8741.93  semi-diameter  ....  3.9416073 
Hence  the  distance  of  Mars  from  the  earth  at  the  time  of  opposition  is  8741.93  of 
the  earth's  semi-diameters;  8741.93:  25'^-  :  23882.84:  9".  15  the  apparent  diam- 
eter of  Mars  if  seen  from  the  earth  at  a  distance  equal  to  that  of  the  sun ;  then 
32'.2/' :  886149  :  :  9".15  :  4218  miles  the  diameter  of  Mars. 

t  The  cube  of  7964,  the  diameter  of  the  earth,  is  505119057344  ;  and  the  cube 
of  4218,  the  diameter  of  Mars,  is  75044648232  ;  the  quotient  produced  by  dividing 
the  former  by  the  latter,  is  6.73.  viz.  the  magnitude  of  the  earth  is  nearly  seven 
times  that  of  Mars. 

J  For,  113:  355:  :  144907630  X  2:  910481569  milBs  the  circumference  of  the 
orbit  of  Mars,  and  686  days  23  h.  15  min.  44  sec.  :  910481569  ra. :  :  1  h.  :  55223 
miles. 

§  In  Plate  IV.  Fig.  8.  let  s  represent  the  sun,  e  the  earth,  and  m  Mars  ;  now,  as 
the  earth  moves  quicker  in  its  orbit  than  Mars,  the  planet  Mars  will  appear  to  go 
backward  when  the  earth  passes  it.  Thus,  when  the  earth  is  at  e.  Mars  will 
appear  among  the  fixed  stars  at  m ;  but  as  the  earth  passes  from  e  to  e,  Mars  will 
appear  to  go  from  m  to  n,  though  he  is  in  reality  travelling  the  same  way  as  the 
earth  from  m  to  o.  The  place  m,  where  Mars  is  seen  from  the  earth  among  the 
fixed  stars,  is  called  his  Geocentric  place,  but  the  place  p,  where  he  would  be 
seen  from  the  sun,  is  called  his  Heliocentric  place,  and  the  arc  m  p,  which  is  the 
difference  between  his  apparent  and  true  place,  is  called  the  Parallax  of  the 
Earth's  annual  Orbit.  Now,  as  this  angle  may  be  determined  from  observa- 
tion, and  is  known  to  be  about  41°  ;  in  the  right-angled  triangle  sem,  we  have 
have  given  se=23882.84  semi-diameters,  the  distance  of  the  earth  from  the  sun, 
the  angle  smb  measured  by  the  arc  m  p=41o,  to  find  sm=36403.49  semi-diameters 
of  the  earth,  the  distance  of  Mars  from  the  sun.  According  to  M.  Laplace,  the 
sidereal  revolution  of  Mars  is  performed  in  686.979619  days,  and  his  mean  distance 
from  the  sun  is  1.523694. 


Chap.  V. 


OP  THE  SOLAR  SYSTEM. 


155 


29th  of  March  1807;  its  distance  from  the  sun  is  225435000* 
miles,  and  the  length  of  its  year,  3  years  240  days  5  hours. 
Vesta  appears  like  a  star,  of  the  fifth  magnitude. 

VII.  Of  Juno 

Juno  was  discovered  by  Mr.  Harding,  of  Lilienthal,  in  the 
duchy  of  Bremen,  on  the  first  of  September,  1804.  It  appears 
like  a  star  of  the  eighth  magnitude ;  its  distance  from  the  sun  is 
253380485  mites,  and  its  periodical  revolution  is  performed  in 
4  years  and  131  days.  ^ 

VIII.  Of  Ceres 

Ceres  was  discovered  by  M.  Piazzi,  astronomer  royal,  at  Pa- 
lermo, in  the  isjand  of  Sicily,  on  the  first  of  January,  1801.  The 
length  of  its  year  is  four  years  221  days  13  hours ;  its  distance 
frQ>m  the  sun  is  262903570  miles,  and  its  diameter,  according  to 
Dr.  H^rschel,  is  about  172  miles.  Ceres  appears  like  a  star  of 
the  eighth  magnitude. 

IX.  Of  Pallas  9. 

Pallas  was  discovered  by  Dr.  Olbers,  on  the  28th  of  March, 
1802.  The  length  of  its  year  is  4  years  221  days  17  hours;  and 
its  distance  from  the  sun  262921240  miles.  Pallas  appears  like 
a  star  of  the  seventh  magnitude,  and  its  diameter  is  stated  to  be 
about  110  miles. 

X.  Of  Jupiter  if,  and  his  Satellites. 

Jupiter  is  the  largest  of  all  the  planets,  and  notwithstanding 
his  great  distance  from  the  sun  and  the  earth,  he  appears  to  the 
naked  eye  almost  as  large  as  Venus,  though  his  light  is  something 
less  brilliant.  Jypiter,  when  in  opposition  to  the  sun,  (that  is, 
when  he  comes  to  the  meridian  at  midnight,  or  rises  when  the 
sun  sets,  and  sets  when  the  sun  rises,)  is  much  nearer  to  the  earth 
than  he  is  a  little  before  and  after  his  conjunction  with  the  sun ; 


♦  Mean  distance  2.373.  The  mean  distance  of  Juno  is  2.667173,  of  Ceres 
2.767406,  of  Pallas  2.767592  according  to  Laplace,  and  the  periods  which  are  given 
from  the  same  author,  are  sidereal  periods. 


156 


OF  THE  SOLAR  SYSTEM. 


Part  II. 


hence,  at  the  time  of  opposition,  he  appears- larger  and  more  lu- 
minous than  at  other  times.  When  the  longitude  of  Jupiter  is 
less  than  that  of  the  sun,  he  will  be  a  morning  star,  and  appear 
in  the  east  before  the  sun  rises  ;  but,  when  his  longitude  is  greater 
than  the  sun's  longitude,  he  will  be  an  evening  star,  and  appear 
in  the  west  after  the  sun  sets.  Jupiter  revolves  on  his  axis  in  9 
hours  56  minutes,  which  is  the  length  of  his  day ;  but  as  his  axis 
is  nearly  perpendicular  to  the  plane  of  his  orbit,  he  has  no  diver- 
sity of  seasons.  Jupiter  is  surrounded  by  faint  substances  called 
zones  or  belts  ;  w^hich,  from  their  frequent  change  in  number  and 
situation,  are  generally  supposed  to  consist  of  clouds.  One  or 
more  dark  spots  frequently  appear  between  the  belts;  and  when 
a  belt  disappears,  the  contiguous  spots  disappear  likewise.  The 
time  of  the  rotation  of  the  different  spots  is  variable,  being  less 
by  six  minutes  near  the  equator  than  near  the  poles.  Dr.  Her- 
schel  has  determined,  that  not  only  the  times  of  rotation  of  the 
different  spots  vary,  but  that  the  time  of  rotation  of  the  same  spot 
(between  the  25th  of  February  1773  and  the  12th  of  April)  varied 
from  9  hours  55  minutes  20  seconds,  to  9  hours  51  minutes  35 
seconds. 

The  inclination  of  the  orbit  of  Jupiter  to  the  pkne  of  the  eclip- 
tic is  1°  18  56  ' ;  the  place  of  his  ascending  node  about  8  degrees 
in  Cancer*  ;  and  he  performs  his  revolution  round  the  sun  in  11 
years  315  days  14  h.  27  m.  11  sec.  moving  at  the  rate  of  29894 
miles  per  hour,  his  mean  distance  from  the  sun  being  494499108 
miles.f  Jupiter,  at  his  mean  distance  from  the  earth,  at  the  time 
of  opposition,  subtends  an  angle  of  46  ,  hence  his  real  diameter 
is  89069  milesj  and  his  magnitude  1400  times  that  of  the  earth. § 


+  The  place  of  Jupiter's  ascending  node  for  the  beginning  of  the  year  1750  was 
70  55'  32  '  in  Cancer,  and  its  variation  in  100  years  is  59'  30  '.    Vince's  Astronomy. 

I  For,  4330  days  14  h.  27  min.  11  sec.= 374 164031  seconds,  the  square  of  which 
is  1 39998722094 16S961 ;  this  divided  by  995S397047971S4,  the  square  of  the  seconds 
in  a  year,  (see  the  note,  page  142,)  gives  140.5S35913,  the  cube  root  of  which  is 
5.1997,  the  relative  distance  of  Jupiter  from  the  sun.  Hence  23882.84  X  5.1997 
=  124183.603148  distance  of  Jupiter  from  the  sun  in  semi-diameters  of  the  earth  ; 
and  124183  603148  X  3982=494499107  7  miles,  the  mean  distance  of  Jupiter  from 
the  sun.  According  to  Laplace  the  sidereal  period  of  Jupiter  is  4332.596303  days, 
and  his  mean  distance  from  the  sun  5.202791. 

Now,  (by  the  note,  page  143,)  113;  355  :  :  494499107.7  X  2  :  3107029791  miles, 
the  circumference  of  the  orbit  of  Jubifer,  and  4330  d.  14  h.  27  min.  11  seconds, 
:  3107029791  :  :  1  h.  :  29894  miles 

X  494499108—95101468  miles  the  distance  of  the  earth  from  the  sun,  =  399397 
640  distance  of  the  earth  from  Jupiter.  Now,  by  the  rule  of  three  inversely, 
399397640:  46"  :  :  95101468  :  193'M862,  the  apparent  diameter  of  Jupiter  at  a  dis- 
tance from  the  earth  equal  to  that  of  the  sun.  Hence,  (as  in  the  note,  page  143,) 
32'  2'' :  886149:  :  193'M862  :  89069.5  miles,  the  diameter  of  Jupiter. 

§  For,  if  the  cube  of  the  diameter  of  Jupiter  be  divided  by  the  cube  of  the  diame- 
ter of  the  earth,  the  quotient  will  be  1398,9  ^  1400  nes^rly. 


Chap.  V. 


OF  THE  SOLAR  SYSTEM. 


157 


The  light  and  heat  which  Jupiter  receives  from  the  sun  is  about 
2V  of  the  hght  and  heat  which  the  earth  receives.* 

On  account  of  the  great  magnitude  of  Jupiter,  and  his  quick 
revolution  on  his  axis,  he  is  considerably  more  flatted  at  the  poles 
than  the  earth  is.  The  ratio  between  his  polar  and  equatorial 
diameters,  has  been  differently  stated  by  different  astronomers  : 
Dr.  Pound  makes  it  as  12  to  13;  Mr.  Short,  as  13  to  14;  Dr. 
Bradley,  as  12|  to  13| ;  and  Sir  Isaac  Newton  (by  theory)  9^  to 
10^. 

Of  tlie  Satellites  of  Jupiter. 

Jupiter  is  attended  by  four  satellites  or  moons,  each  of  which 
revolves  round  him  in  a  manner  similar  to  that  of  the  moon  round 
the  earth.  The  times  of  their  periodical  revolutions  round  Ju- 
piter, and  their  respective  distances,  from  his  centre,  are  given 
in  the  following  table  :f 


Satellites. 

Periodical  revolution. 

Distance  from  Ju- 
piter in  semi-diam- 
eters. 

Distance  from 
Jupiter  in  Eng- 
lish miles. 

d.    h.     m,  sec. 

I. 

1  .  18. 27. 33 

5.67 

252510 

11. 

3.  13.  13.42 

9.00 

400810 

III. 

7.  3.42.33 

14.38 

640406 

IV. 

16.16.32.  8 

25.30 

1126723 

The  satellites  of  Jupiter  are  invisible  to  the  naked  eye  ;  they 
were  first  discovered  by  Galileo,  the  inventor  of  telescopes,  in  the 
year  1610.  This  was  an  important  discovery ;  for,  as  these  sat- 
ellites revolve  round  Jupiter  in  the  same  direction  which  Jupi- 
ter revolves  round  the  sun,  they  are  frequently  eclipsed  by  his 
shadow,  and  afford  an  excellent  method  of  finding  the  true  lon- 


*  If  the  square  of  the  mean  distance  of  Jupiter  from  the  sun  be  divided  by  the 
square  of  the  mean  distance  of  the  earth  from  the  sun,  the  quotient  will  be  27. 

t  The  second  and  third  columns  in  the  above  table  are  copied  from  M.  de  la 
Lande,  and  the  fourth  is  found  by  multiplying  the  numbers  in  the  third  column  by 
44534,5,  being  the  half  of  89069,  the  diameter  of  Jupiter.  The  distances  of  the 
satellites  from  the  centre  of  Jupiter  may  be  found  at  the  time  of  their  greatest  elon- 
gations, by  measuring  their  distances  from  the  centre  of  Jupiter,  and  also  the  diam- 
eter of  Jupiter  with  a  micrometer.  Then  say,  as  the  apparent  diameter  of  Jupiter 
(by  the  micrometer)  is  to  his  real  diameter,  so  is  the  apparent  distance  of  the  sat- 
ellite to  its  real  distance.  Or,  having  determined  the  periodical  times  of  the  satel- 
lites, and  the  distance  of  one  of  them'from  the  sun,  the  distances  of  all  the  rest  may 
be  found  by  Kepler's  rule,  as  in  page  142. 


158 


OF  THE  SOLAR  SYSTEM. 


Part  II. 


gitudes  of  places  on  the  land.  To  these  eclipses  we  likewise  owe 
the  discovery  of  the  progressive  motion  of  light,  and  hence  the 
aberration  of  the  fixed  stars. 

The  satellites  of  Jupiter  do  not  revolve  round  bim  in  the  same 
plane,  neither  are  their  nodes  in  the  same  place.  These  satel- 
lites appear  of  different  magnitudes  and  brightness,  the  fourth  gen- 
erally appears  the  smallest,  but  sometimes  the  largest,  and  the 
apparent  diameter  of  its  shadow  on  Jupiter  is  sometimes  greater 
than  the  satellite.  M.  Cassini  and  Mr.  Pound  supposed  that  the 
satellites  of  Jupiter  revolved  on  their  axes  ;  and  Dr.  Herschel  has 
discovered  that  they  revolve  about  their  axes  in  the  time  in  which 
they  respectively  revolve  about  Jupiter. 

The  first  satellite  is  the  most  important  of  the  fbur,  from  its 
numerous  eclipses.  The  times  of  the  eclipses  of  the  satellites  of 
Jupiter  are  calculated  for  the  ^eridian  of  Greenwich,  and  insert- 
ed in  the  Illd  page  of  the  Nautical  Almanac  for  every  month,  and 
their  configuration  or  appearances,  with  respect  to  Jupiter,  are 
inserted  in  page  XII.  As  the  ea4h  turns  on  its  axis  from  west  to 
east  at  the  rate  of  15  degrees  in  an  hour,  or  one  degree  in  four 
minutes  of  time,  a  person  one  degree  westward  of  Greenwich, 
will  observe  the  immersion  or  emersion  of  any  one  of  the  satellites 
of  Jupiter  four  minutes  later  than  the  time  menfion^  in  the 
Nautical  Almanac ;  and,  if  he  be  one  degree  eastward  of  Green- 
wich, the  echpse  will  happen  four  minutes  sooner  at  his  place 
of  observation  than  at  Greenwich.  These  echpses  must  be  ob- 
served with  a  good  telescope  and  a  pendulum  clock  which  beats 
seconds  or  half-seconds. 

The  configurations  of  the  satellites  of  Jupiter  at  eight  o'clock 
at  night  in  the  month  of  March,  and  in  the  year  1825,  are  given 
in  the  Xllth  page  of  the  Nautical  Almanac  as  in  the  following 
page  ;  an  explanation  of  which  will  render  the  Xllth  page  of  that 
work  intelligible  to  a  young  student  for  any  other  year  and  month. 

Jupiter  is  distinguished  by  the  mark  O,  and  the  satellites  by 
points  with  figures  annexed ;  the  figure  1  signifying  the  first  satel- 
lite, 2  the  second,  &c.  When  the  satellite  is  approaching  Jupiter, 
the  figure  is  placed  between  Jupiter  and  the  point ;  and  when  the 
satellite  is  receding  from  Jupiter,  the  point  is  placed  between  the 
figure  and  Jupiter; 


Chap.  V. 


OF  THE  SOLAR  SYSTEM. 


159 


4. 

l.ii)2.«  2 

0 

•4 

5. 

.3  .2 

0 

.1 

.4 

6. 

.3  0 

1.® 

.2 

4. 

8. 

1  62 

0 

4. 

3. 

9.  ^ 

.2 

4. 

0 

1. 

3. 

11. 

4.  3. 

0 

2. 

1.  • 

14. 

.4 

0 

.1 

2  6  3 

On  the  fourth  day  of  the  month,  given  above,  the  first  and  sec- 
ond satellites  are  eclipsed  at  eight  at  night ;  the  thiixl  is  on  the 
left  hand  of  Jupiter,  and  receding  from  the  planet,  and  the  fouKlh 
is  on  the  right  hand  receding. 

On  the  fifth  day  of  the  month,  at  the  same  hour,  the  third  and 
second  satellites  are  on  the  left  hand  of  Jupiter,  and  are  ap- 
proaching him ;  the  first  is  on  the  right  hand  receding  from  the 
planet,  and  the  fourth  is  on  the  right  hand  approaching  it. 

On  the  sixth  day  the  third  satellite  v^ill  appear  like  a  bright 
spot  on  the  disc  of  Jupiter ;  the  first  will  be  on  the  left  hand  re- 
ceding from  Jupiter ;  the  second  and  fourth  on  the  right  hand,  the 
second  receding  from,  and  the  fourth  approaching  the  planet. 

On  the  eigth  day  the  first  and  second  satellites  are  in  conjunc- 
tion on  the  left  hand  of  Jupiter ;  the  fourth  and  third  are  on  the 
right  hand  approaching  the  planet. 

On  the  fourteenth  day  the  fourth  satellite  is  on  the  left  hand  ap- 
proaching Jupiter,  the  first  on  the  right  hand  receding  from  Jupi- 
ter, and  the  second  and  third  in  conjunction  on  the  right  hand. 

By  observations  on  the  satellites  of  Jupiter  the  progressive  mo- 
tion of  light  was  discovered  ;  for  it  has  been  found  by  repeated  ex- 
periments ;  that,  when  the  earth  is  exactly  between  Jupiter  and 
the  sun,  the  eclipses  of  Jupiter's  satellites  are  seen  8^  minutes 
later  than  the  t|^e  predicted ;  hence  it  is  inferred  that  light  takes 
up  about  16|  minutes  of  time  to  pass  over  a  space  equal  to  the 


( 


160 


01?  THE  SOLAR  SYSTEM. 


Part  11. 


diameter  of  the  earth's  annual  orbit,  which  is  190  millions  of 
miles,  or  double  of  the  distance  of  the  earth  from  the  sun  ;  for  if 
the  effects  of  light  were  instantaneous,  the  eclipses  of  the  satel- 
lites would  in  all  situations  of  the  earth  in  its  orbit  happen  ex- 
actly at  the  time  predicted  by  calculation. 

Of  Saturn  ^  his  Satellites  and  Ring, 

Saturn  shines  with  a  pale,  feeble  light,  being  the  farthest  from 
the  sun  of  any  of  the  planets  that  are  visible  without  a  telescope. 
This  planet,  when  viewed  through  a  good  telescope,  always  en- 
gages the  attention  of  the  young  astronomer  by  the  singularity  of 
its  appearance.  It  is  surrounded  by  an  interior  and  exterior  ring, 
beyond  which  are  seven  satellites  or  moons,  all,  except  one,  in 
the  same  plane  with  the  rings.  These  rings  and  satellites  are  all 
opaque  and  dense  bodies,  like  that  of  Saturn,  and  shine  only  by 
the  light  which  they  receive  from  the  sun.  The  disc  of  Saturn  is 
likewise  crossed  by  obscure  zones  or  belts,  like  those  of  Jupiter, 
which  vary  in  their  figure  according  to  the  direction  of  the  rings. 
Saturn  performs  his  revolution  round  the  sun  in  29  years  174  days 
1  hour  51  minutes  11  seconds*  ;  hence  his  mean  distance  from 
the  sun  is  907089032  milesf ;  and  his  progressive  motion  in  his 
orbit  is  22072  miles  per  hour. 

The  inclination  of  the  orbit  of  Saturn  to  the  plane  of  the 
ecliptic  is  said  to  be  2°  29'  50",  and  the  place  of  his  ascending 
node  about  21  degrees  in  Cancer.J 

Saturn,  at  his  mean  distance  from  the  earth,  subtends  an  angle 


*  Laplace  states  the  sidereal  period  of  Saturn  to  be  10738  96984  days,  and  his 
mean  distance  from  the  sun  9.53877  ;  see  also  Jlbreges  d?  Astronomie,  par  M.  De- 
lambre,  page  432.    Paris,  1813. 

t  For  10759  d.  1  h.  51  min.  11  sec.=929584271  seconds,  the  square  of  which  is 
864126916890601441,  this  divided  by  995839704797184,  the  square  of  the  seconds 
in  a  year  (see  the  note,  pagel42.)  gives  867,736958,  the  cube  root  of  which  is 
9.5381 18,  the  relative  distance  of  Saturn  from  the  sun.  Hence  23382.84  X  9.531 18 
=227797.34609512  distance  of  Saturn  from  the  sun  in  semi-diameters  of  the  earth; 
and  227797.34609512  X3982=907089032.15  miles,  the  mean  distance  of  Saturn 
from  the  sun.  113  :  355  :  907089032  X  2  :  5699408962.1238  miles  circumference  of 
the  orbit  of  Saturn.  Then,  10759  d.  Ih.  51m.  II  sec.  :  5699408962  miles  :  :  1  h.  : 
22072  miles  which  Saturn  moves  per  hour  in  his  orbit. 

I  The  place  of  Saturn's  ascending  node  for  the  beginning  of  the  year  1750 
was  21°  32'  22''  in  Cancer,  and  its  variation  in  100  years  is  55'  30".  Vince's  As- 
tronomy. 


Chap.  V. 


OF  THE  SOLAR  SYSTEM. 


161 


of  20";  hence  his  real  diameter  is  78730*  miles  and  his  magni- 
tude 966t  times  that  of  the  earth.  The  light  and  heat  which  this 
planet  receives  from  the  sun  is  about  partj  of  the  light  and 
heat  which  the  earth  receives. 

According  to  Dr.  Herschel,  Saturn  revolves  on  his  axis  from 
west  to  east  in  10  hours  16  min.  2  sec.  and  this  axis  is  perpendic- 
ular to  the  plane  of  his  ring.  The  equatorial  diameter  of  Saturn, 
viz.  the  diameter  in  the  direction  of  the  ring,  is  to  the  polar  diam- 
eter, viz.  the  axis,  as  11  to  10. 

Of  the  Satellites  of  Saturn, 

Saturn  is  attended  by  seven  moons ;  the  fourth  was  discovered 
be  Huygens,  a  Dutch  mathematician,  in  the  year  1655.  The 
first,  second,  third,  and  fifth,  were  discovered  at  different  times, 
between  the  years  1671  and  1685,  by  Cassini,  a  celebrated  Ital- 
ian astronomer.  The  sixth  and  seventh  satellites  were  discovered 
by  Dr.  Herschel  in  the  years  1787  and  1789.  The  two  satellites 
discovered  by  Dr.  Herschel  are  nearer  to  Saturn  than  the  other 
five,  and  therefore  should  be  called  the  first  and  second ;  but  to 
distinguish  them  from  the  other  satelHtes,  and  to  prevent  confu- 
sion in  referring  to  former  observations,  they  are  called  the  sixth 
and  seventh  satellites.  The  seventh  satellite,  which  is  nearest  to 
Saturn,  was  discovered  a  short  time  after  the  sixth.  In  the  fol- 
lowing table,  the  satellites  are  arranged  according  to  their  re- 
spective distances  from  Saturn,  and  the  Roman  figures  in  the  left- 
hand  column  show  the  number  of  the  satellite.  The  figures  be- 
tween the  parentheses  show  the  order  in  which  they  ought  to  be 
numbered. 


*  907089032—95101468  miles,  the  distance  of  the  earth  from  the  sun,  = 
811987564  miles  distance  of  the  earth  from  Jupiter.  Now,  inversely,  811987564 
:  20"  :  :  95101468:  170''.762,  the  apparent  diameter  of  Saturn  at  a  distance  from 
the  earth  equal  to  that  of  the  sun  (by  the  note,  page  143) ;  32'  2"  :  886149 
;  :  170''.762  :  78730  miles,  the  diameter  of  Saturn. 

•f  Found  by  dividing  the  cube  of  the  diameter  of  Saturn  by  the  cube  of  the  diam- 
eter of  the  earth. 

I  Found  by  dividing  the  square  of  the  mean  distance  of  Saturn  from  the  sun  by 
the  square  of  the  earth's  mean  distance  from  the  sun. 


r 


21 


162 

OF  THE  SOLAR 

SYSTEM. 

Part  11. 

Distance  from 

Distance  from 

Satellites. 

Periodical  revolution. 

Saturn  in  serai- 

Saturn  in  Eng- 

CllcHUt/lt;!  o 

from  Laplace* 

d.     h.       m.  sec. 

YII. 

(1) 

0  .  22  .  37  .  23 

3.080 

121244 

YI. 

(2) 

1  .    8  .  63  .  9 

3.952 

155570 

I. 

(3) 

1  .  21  .  18  .  27 

4.893 

192613 

II. 

(4) 

2  .  17  .  44  .  51 

6.268 

246740 

III. 

(5) 

o.  /  04t 

o4:4tDUl 

IV. 

(6) 

15  .  22  .  41  .  16 

20.295 

798912 

V. 

(7) 

79  .    7  .  53  .  43 

59.154 

2328597 

The  first,  second,  third,  and  fourth  satelhtes,  as  well  as  the 
sixth  and  seventh,  are  all  nearly  in  the  same  plane  with  Saturn's 
ring,  and  are  inclined  to  the  orbit  of  Saturn  in  an  angle  of  about 
30  degrees  ;  but  the  orbit  of  the  fifth  satellite  is  said  to  make  an 
angle  of  fifteen  degrees  w^ith  the  plane  of  Saturn's  ring.  Sir 
Isaac  Newton  conjectured*  that  the  fifth  satellite  of  Saturn  re- 
volved round  its  axis  in  the  same  time  that  it  revolved  round 
Saturn ;  and  the  truth  of  his  opinion  has  been  verified  by  the  ob- 
servations of  Dr.  Herschel. 

Of  SaturvLS  Ring. 

The  ring  of  Saturn  is  a  thin,  broad,  and  opaque  circular  arch, 
surrounding  the  body  of  the  planet  without  touching  it,  like  the 
wooden  horizon  of  an  artificial  globe.  If  the  equator  of  the  ar- 
tificial globe  be  made  to  coincide  with  the  horizon,  and  the  globe 
be  turned  on  its  axis  from  west  to  east,  its  motion  will  represent 
that  of  Saturn  on  its  axis,  and  the  wooden  horizon  will  represent 
the  ring,  especially  if  it  be  supposed  a  little  more  distant  from  the 
globe.  The  ring  of  Saturn  was  first  discovered  by  Huygens  ;  and 
"when  viewed  through  a  good  telescope,  appears  double.  Dr. 
Herschel  says,  that  Saturn  is  encompassed  by  two  concentric 
rings,  of  the  following  demensions : 

Miles. 

Inner  diameter  of  the  smaller  ring  -  -  146345 

Outside  diameter  of  ditto  -  -  -  184393 

Inner  diameter  of  the  larger  ring  -  -  190248 


+  Principia,  Book  III.  Prop.  xvii. 


Chap,  V. 


OF  THE  SOLAR  SYSTEM. 


163 


Outside  diameter  of  ditto  -  -  -  204883 

Breadth  of  the  inner  ring  -  -  -  20000 

Breadth  of  the  outer  ring  -  -  -  7200 

Breadth  of  the  vacant  space,  or  dark  zone  between  the 

rings  _____  2839 

The  ring  of  Saturn  revolves  round  his  axis  and  in  a  plane  co- 
incident w^ith  the  plane  of  his  equator,  in  10  hours  32  min.  15.4 
sec.  The  ring  being  a  circle,  appears  elliptical,  from  its  oblique 
position  ;  and  it  appears  most  open  w^hen  Saturn's  longitude  is 
about  2  signs  17  degrees,  or  8  signs  17  degrees.  There  have 
been  various  conjectures  relative  to  the  nature  and  properties  of 
this  ring. 

XII.  Of  the  Georgium  Sidus,  or  Herschel       and  its 

Satellites. 


The  Georgian  is  the  remotest  of  all  the  known  planets  belong- 
ing to  the  solar  system  ;  it  was  discovered  at  Bath  by  Dr.  Her- 
schel on  the  13th  of  March,  1781.  This  planet  is  called  by  the 
English  the  Georgium  Sidus,  or  Georgian,  a  name  by  which  it  is 
distinguished  in  the  Nautical  Almanac.  It  is  frequently  called  by 
foreigners  Herschel,  in  honour  of  the  discoverer.  The  royal 
academy  of  Prussia,  and  some  others,  called  it  Ouranus,  because 
the  other  planets  are  named  from  such  heathen  deities  as  were 
relatives :  thus  Ouranus  was  the  father  of  Saturn,  Saturn  the 
father  of  Jupiter,  Jupiter  the  father  of  Mars,  &:c.  This  planet, 
when  viewed  through  a  telescope  of  a  small  magnifying  power, 
appears  like  a  star  of  between  the  6th  and  7th  magnitudes.  In 
a  very  fine  clear  night,  in  the  absence  of  the  moon,  it  may  be 
perceived,  by  a  good  eye,  without  a  telescope.  Though  the 
Georgium  Sidus  was  not  known  to  be  a  planet  till  the  time  of 
Dr.  Herschel,  yet  astronomers  generally  believe  that  it  has  been 
seen  long  before  his  time,  and  considered  as  a  fixed  star.* 

In  so  recent  a  discovery  of  a  planet  at  such  an  immense  dis- 
tance, the  theory  of  its  magnitude,  motion,  &c.  must  be  in  some 


*  According  to  F.  de  Zach's  account  of  this  planet  in  the  Memoirs  of  the 
Brussels  Academy,  1785,  there  was  then  in  the  library  of  the  Prince  of  Orange, 
four  observations  of  this  planet  considered  as  a  star,  in  a  catalogue  of  observations 
written  by  Tycho  Brahe  ;  but,  as  Tycho  was  not  acquainted  with  the  use  of 
telescopes,  some  writers  contend  that  he  could  not  see  it  ;  while  others  maintain 
that,  as  he  has  marked  stars  which  are  not  greater  than  this  planet,  he  might  cer- 
tainly have  seen  it.  This  planet  was.  likewise  seen  by  Professor  Mayer  of 
Gottingen,  in  the  year  1756,  being  the  964th  of  his  catalogue. 


/  ON  COMETS.  Part  II. 

nnperfect.  Its  periodical  revolution  round  the  sun  is  said 
to  be  pxJrformed  in  83  years  150  days  18  hours  the  ratio  of  its 
diameter  to  that  of  the  earth,  is  as  4.32  to  1  ;  consequently  its 
magnitude  is  upwards  of  eighty  times  that  of  the  earth. 

The  Georgian  planet  is  attended  by  six  satellites  ;  their  period- 
ical revolutions  and  times  of  discovery  are  as  follow : 

d.    h.    m.  s. 

ML     I.  or  nearest,  revolves  in      >5  21  25    0,  discovered  in  1798 


II.  -  -  8  17  1  19,  discovered  in  1787 

III.  -  -  10  23  4    0,  discovered  in  1798 

IV.  -  -  13  11  5  11,  discovered  in  1787 

V.  ^  -  -  38    1  49    0,  discovered  in  1798 

VI.  -  -  107  Ki  40    0,  discovered  in  1798 


All  these  satellites  were  discovered  by  Dr.  Herschel ;  their 
orbits  are  said  to  be  nearly  perpendicular  to  the  ecliptic,  and 
what  is  more  singular,  they  perform  their  revolutions  round  the 
Georgian  planet  in  a  retrograde  order,  viz.  contrary  to  the  order 
of  the  signs. 


CHAPTER  VI. 

On  the  Nature  of  Comets ;  the  Elongations,  Stationary,  and  Ret- 
rograde Appearance  of  the  Planets ;  and  on  the  Eclipses  of  the 
Sun  and  Moon, 

On  Comets. 

Though  the  primary  planets  already  described,  and  their 
satellites,  are  considered  as  the  whole  of  the  regular  bodies  which 
form  the  solar  system,  yet  that  system  is  sometimes  visited  by 
other  bodies,  called  comets,  which  are  supposed  to  move  round 
the  sun  in  elliptical  orbits.  These  orbits  are  supposed  to  have 
the  sun  in  one  of  the  foci,  like  the  planets ;  and  to  be  so  very 
eccentric,  that  the  comet  becomes  invisible  when  in  that  part  of 


*  According  to  Laplace,A.he  sidereal  period  of  the  Georgian  is  30688.712687  days, 
and  its  mean  distance  from  the  earth  19.183305. 


Chap,  VL 


ON  COMETS. 


165 


its  orbit  which  is  the  farthest  from  the  sun.  It  is  extremely  diffi- 
cult to  deterrnine  the  elliptic  orbit  of  a  comet,  with  any  degree  of 
accuracy  by  calculation  ;  for,  if  the  orbit  be  very  eccentric,  a 
small  error  in  the  observation  will  change  the  computed  orbit  into 
a  parabola  or  hyperbola;  and  from  the  thickness  and  inequality 
of  the  atmosphere  with  which  a  comet  is  surrounded,  telescopic 
observations  on  them  are  always  liable  to  error.  Hence  the  the- 
ory of  the  orbits,  motions,  &c.  of  comets,  is  very  imperfect ;  and 
though  many  volumes  have  been  written  on  the  subject*,  they  are 
chietly  founded  on  conjecture.  The  unexpected  appearance  of 
the  comet  in  1807  fully  confirms  this  assertion,  and  will  doubtless 
give  rise  to  a  variety  of  new  calculations,  and  new  hypotheses, 
which,  like  former  ones,  for  want  of  sufficient  data,  will  disappoint 
the  expectations  of  succeedins:  astronomers.  The  same  observa- 
tions will  apply  to  the  very  brilliant  comet  which  appeared  in  the 
months  of  September,  October,  and  November,  1811.  Among 
all  the  different  comets  that  have  appeared,  the  period  of  only  one 
of  them  is  known  with  any  degree  of  accuracy,  viz.  that  which 
was  observed  in  1531,  1607,  and  1682,  being  about  76  years. 
The  comets.  Sir  Isaac  Newtonf  observes,  are  compact,  solid,  and 
durable  bodies,  or  a  kind  of  planets  which  move  in  very  oblique 
and  eccentric  orbits  every  way  with  the  greatest  freedom,  and 
preserve  their  motions  for  an  exceeding  long  time,  even  where 
contrary  to  the  course  of  the  planets.  Their  tail  is  a  very  thin 
and  slender  vapour,  emitted  by  the  head  or  nucleus  of  the  comet 
when  ignited  or  heated  by  the  sun,         ^  1''^ 

II.  Of  the  Elongations,  &c.  of  the  interior  Planets. 

Let  T,  E,  e,  {Plate  IV.  Fig.  8,)  represent  the  orbit  of  the  earth  ; 
a,  w,  V,  X,  /,  g,  h,  the  orbit  of  an  interior  planet,  as  Mercury  or 
Venus,  and  s  the  sun. 

Let  T  represent  the  earth,  s  the  sun,  and  cz  Venus  at  the  time  of 
her  inferior  conjunction  ;  at  this  time  she  will  disappear  like  the 
new  moon,  because  her  dark  side  will  be  turned  towards  the 


+  The  latest  writings  on  the  subject  of  comets  are  M.  Pingre's  Comctographie, 
in  two  vols.  4to.,  and  Sir  Henry  Englefield's  work,  entitled,  "  On  the  Determina- 
tion of  the  Orbits  of  Comets.  A  well  written  article  on  Comets  may  be  seen  in 
Dr.  Rees'  JVau  Cyclopedia,  together  with  the  elements  of  ninety-seven  of  them,  and 
the  names  of  the  autliors  who  have  calculated  their  orbits. 

fMany  interesting  particulars  respecting  the  nature  of  comets,  &c.  may  be  learned 
by  referring  to  the  latter  end  of  the  third  book  of  Newton's  Principia. 


1(36 


OF  THE  ELONGATIONS,  4^C. 


Part  II. 


earth.  While  Venus  moves  from  a  towards  w  she  appears  to  the 
westward  of  the  sun,  and  becomes  gradually  more  and  more  en- 
lightened (having  all  the  different  phases  of  the  moon.)  When 
she  arrives  at  v,  her  greatest  elongation,  she  appears  half  enlight- 
ened, like  the  moon  in  her  first  quarter ;  at  this  time  she  shines 
very  bright.*  From  her  inferior  to  her  superior  conjunction,  viz. 
from  her  situation  in  that  part  of  her  orbit  which  is  directly  be- 
tween the  earth  and  the  sun  as  at  a,  to  her  situation  in  that  part  of 
her  orbit  in  which  the  sun  is  between  her  and  the  earth ;  she  rises 
before  the  sun  in  the  morning,  and  is  called  a  morning  star.  From 
her  superior  to  her  inferior  conjunction  she  shines  in  the  evening 
after  the  sun  sets,  and  is  then  called  an  evening  star. 

From  the  greatest  elongation  of  Venus  when  westward  of  the 
sun,  as  at  to  her  greatest  elongation  when  eastward  of  the  sun 
as  at  g,  she  will  appear  to  go  forward  in  her  orbit,  and  describe 
the  arc  vwhg  amongst  the  fixed  stars  ;  but  from  g  to  v  she  will 
appear  retrogradef,  or  return  to  the  point  v  in  the  heavens  in  the 
order  ghwv.  For  when  Venus  is  at  /,  she  will  be  seen  amongst 
the  fixed  stars  at  ii,  and  w^hen  at  g,  she  will  appear  at  g  :  when  she 
arrives  at  she  will  again  appear  at  h  in  the  heavens.  Hence  in 
a  considerable  part  of  her  orbit  between  f  and  and  between  w 
and  X,  she  will  appear  nearly  in  the  same  point  amongst  the  fixed 
stars,  and  at  these  times  is  said  to  be  stationary.J 

When  a  planet  appears  to  move  from  the  neighbourhood  of  any 
fixed  stars,  towards  others  which  He  to  the  eastward,  its  motion  is 
said  to  be  direct ;  when  it  proceeds  towards  the  stars  which  lie 
to  the  west,  its  motion  is  retrograde  ;  and  when  it  seems  not  to 
alter  its  position  amongst  the  fixed  stars,  it  is  said  to  be  stationary. 

If  the  earth  stood  still  at  t,  the  planet  Venus  would  seem  to 
make  equal  vibrations  from  the  sun  each  way,  forming  the  equal 
angles  ^ts  and  fTs,  each  47°  48',  her  greatest  elongation,  and  the 
stationary  points  would  always  be  in  the  same  place  in  the 
heavens ;  but  it  must  be  remembered  that,  while  Venus  is  pro- 


*  Venus  gives  the  greatest  quantity  of  light  to  the  earth  when  her  elongation  is 
390  44/    Fince's  Fluxions. 

t  The  stationary  and  retrograde  appearances  of  the  inferior  planets  are  neatly 
illustrated  by  a  small  orrery,  made  and  sold  by  Messrs  "W.  and  S.  Jones,  Mathe- 
matical Instrument-makers,  Holborn. 

X  This  manner  of  determining  the  stationary  points  is  the  same  with  that  given 
by  Ferguson  in  his  Astronomy,  Enfield  in  his  Philosophy,  and  by  many  other  wri- 
ters who  were  neither  mathematicians  nor  practical  astronomers.  For  an  accurate 
and  extensive  view  of  this  subject  see  Emerson's  Astronomy,  Vince's  large  Astron- 
omy, vol.  I.  and  Delambre's  large  Astronomy,  vol.  III. 


Chap,  VI. 


OF  THE  ELONGATIONS,  ^C. 


167 


ceeding  in  her  orbit  from  a  towards  x,  the  earth  is  going  forward 
from  T  towards  e  ;  hence  the  stationary  points,  and  places  of  con- 
junction and  opposition,  vary  in  every  revohition. 

What  has  been  observed  with  respect  to  Venus,  may  be  ap- 
phed  with  a  httle  variation  to  Mercury. 

III.  Of  the  stationary  and  retrograde  appearances  of 

THE  EXTERIOR  PlANETS. 

Because  the  earth's  orbit  is  contained  within  the  orbit  of  Mars, 
Jupiter,  &c.  they  are  seen  in  all  sides  of  the  heavens,  and  are  as 
often  in  opposition  to  the  sun  as  in  conjunction  with  him.  Let 
the  circle  in  which  t  is  situated  {Plate  IV.  Fig.  8.)  represent  the 
orbit  of  the  earth,  and  that  in  which  m  is  situated  the  orbit  of  Mars. 
Now,  if  the  earth  be  at  t  when  Mars  is  at  m,  Mars  and  the  sun 
will  be  in  conjunction,  but  if  the  earth  be  at  t  when  Mars  is  at  m, 
they  will  be  in  opposition,  viz.  the  sun  will  appear  in  the  east 
when  Mars  is  in  the  west.  If  the  earth  stood  still  at  t,  the  motion 
of  the  planet  Mars  would  always  appear  direct;  but  the  motion  of 
the  earth  being  more  rapid  than  that  of  Mars,  he  will  be  overtaken 
and  passed  by  the  earth.  Hence  Mars  will  have  two  stationary 
and  one  retrograde  appearance.  Suppose  the  earth  to  be  at  e 
when  Mars  is  at  m,  he  will  be  seen  in  the  heavens  among  the  fixed 
stars  at  m ;  and  for  some  time  before  the  earth  has  arrived  at  e, 
and  after  it  has  passed  e,  he  will  appear  nearly  in  the  same  point 
m,  viz.  he  will  be  stationary.  While  the  earth  moves  through  the 
part  E  i  e  of  its  orbit,  if  Mars  stood  still  at  m,  he  would  appear  to 
move  in  a  retrograde  direction  through  the  arc  m  p  r  n,  in  the 
heavens,  and  would  again  be  stationary  at  n ;  but  if,  during  the 
time  the  earth  moves  from  e  to  e,  Mars  moves  from  m  to  o,  the 
arc  of  retrogradation  would  be  nearly  mv  r. 

The  same  manner  of  reasoning  may  be  applied  to  Jupiter  and 
all  the  superior  planets.  ? 

IV.  On  Solar  and  Lunar  Eclipses. 

An  eclipse  of  the  sun  is  occasioned  by  the  dark  body  of  the  moon 
passing  between  the  earth  and  the  sun,  or  by  the  shadow  of  the 
moon  falling  on  the  earth  at  the  place  where  the  observer  is  sit- 
uated, hence  all  the  eclipses  of  the  sun  happen  at  the  time  of  the 
new  moon.  Thus,  let  s  represent  the  sun,  (Plate  II.  Fig.  6.)  m 
the  moon  between  the  earth  and  the  sun,  «  e  g  6  a  portion  of  the 
earth's  orbit,  e  and  /  two  places  on  the  surface  of  the  earth.  The 
dark  part  of  the  moon's  shadow  is  called  the  umbra,  and  the  light 


168 


ON  SOLAR  AND  LUNAR  ECLIPSES. 


Part  II. 


part  the  penumbra ;  now  it  is  evident  that  if  a  spectator  be  situated 
in  that  part  of  the  earth  where  the  umbra  falls,  that  is  between 
e  and  /,  there  will  be  a  total  eclipse  of  the  sun  at  that  place  ;  at  e 
and  /  in  the  penumbra  there  will  be  ^partial  eclipse;  and  be- 
yond the  penumbra  there  will  be  no  eclipse.  As  the  earth  is  not 
always  at  the  same  distance  from  the  moon,  if  an  eclipse  should 
happen  when  the  earth  is  so  far  from  the  moon  that  the  lines  f  e 
and  c  /  cross  each  other  before  they  come  to  the  earth,  a  specta- 
tor situated  on  the  earth,  in  a  direct  line  between  the  centres  of 
the  sun  and  moon,  would  see  a  ring  of  light  round  the  dark  body 
of  the  moon,  called  an  annular  eclipse  :  when  this  happens  there 
can  be  no  total  eclipse  any  where,  because  the  moon's  umbra  does 
not  reach  the  earth.  People  situated  in  the  penumbra  will  per- 
ceive a  partial  eclipse. 

According  to  M.  de  Sejour,  an  eclipse  can  never  be  annular 
longer  than  12  min.  24  sec,  nor  total  longer  than  7  min  58  sec. 
If  the  moon  be  exactly  in  her  node,  the  centre  of  her  shadow  will 
pass  over  the  centre  of  the  earth's  enlightened  disc,  and  describe 
a  diameter,  if  the  moon  has  latitude,  the  centre  of  her  shadow  will 
describe  a  chord  on  the  circular  disc  of  the  earth,  varying  in  length 
according  to  her  latitude :  hence  the  duration  of  a  solar  eclipse 
depends  on  the  length  of  the  line  which  the  centre  of  her  shadow 
describes,  the  proximity  of  the  place  to  the  centre  of  the  earth's 
disc,  and  the  velocity  of  the  moon's  motion. 

As  the  sun  is  not  deprived  of  any  part  of  his  light  during  a  solar 
eclipse,  and  the  moon's  shadow,  in  its  passage  over  the  earth 
from  w^est  to  east,  only  covers  a  small  part  of  the  earth's  enlight- 
ened hemisphere  at  once,  it  is  evident  that  an  eclipse  of  the  sun 
may  be  invisible  to  some  of  the  inhabitants  of  the  earth's  enlight- 
ened hemisphere,  and  a  partial  or  total  eclipse  may  be  seen  by 
others  at  the  same  moment  of  time. 

An  eclipse  of  the  moon  is  caused  by  her  entering  the  earth's 
shadow,  and  consequently  it  must  happen  when  she  is  in  opposi- 
tion to  the  sun,  that  is,  at  the  time  of  full  moon,  when  the  earth 
is  between  the  sun  and  the  moon.  Let  s  represent  the  sun 
{Plate  II.  Fig.  6.)  eg  the  earth,  and  m  the  moon  in  the  earth's 
umbra,  having  the  earth  between  her  and  the  sun ;  dep  and  hgp 
the  penumbra.  Now,  the  nearer  any  part  of  the  penumbra  is  to 
the  umbra,  the  less  light  it  receives  from  the  sun,  as  is  evident  from 
the  figure ;  and  as  the  moon  enters  the  penumbra  before  she  en- 
ters the  umbra,  she  gradually  loses  her  light  and  appears  less 
brilliant. 

The  duration  of  an  eclipse  of  the  moon,  from  her  first  touching 
the  earth's  penumbra  to  her  leaving  it,  cannot  exceed  51-2  hours. 


€hap.  VI. 


ON  SOLAR  AND  LUNAR  ECLIPSES. 


169 


The  moon  cannot  continue  in  tlie  earth's  umbra  longer  than  3| 
hours  in  any  eclipse,  neither  can  she  be  totally  eclipsed  for  a 
longer  period  than  if  hour.*  As  the  moon  is  actually  deprived 
of  her  light  during  an  eclipse,  every  inhabitant  upon  the  face  of 
the  earth  who  can  see  the  moon  will  see  the  eclipse. 

General  Observations  on  Eclipses.  ' 

If  the  orbit  of  the  earth  and  that  of  the  moon  were  both  in  the 
same  plane,  there  would  be  an  eclipse  of  the  sun  at  every  new 
moon,  and  an  eclipse  of  the  moon  at  every  full  moon.  But  the 
orbit  of  the  moon  makes  an  angle  of  about  5^  degrees  with 
the  plane  of  the  orbit  of  the  earth,  and  crosses  it  in  two  points 
called  the  nodes ;  now  astronomers  have  calculated  that,  if  the 
moon  be  less  than  17°  21'  from  either  node,  at  the  time  of  new 
moon,  the  sun  may  be  eclipsed  ;  or  if  less  than  11°  34'  from  either 
node,  at  the  full  moon,  the  moon  may  be  eclipsed  ;  at  all  other 
times,  there  can  be  no  eclipse,  for  the  shadow  of  the  moon  will 
fall  either  above  or  below  the  earth  at  the  time  of  new  moon ; 
and  the  shadow  of  the  earth  will  fall  either  above  or  below  the 
moon  at  the  time  of  full  moon.  To  illustrate  this,  suppose  the 
right-hand  part  of  the  moon's  orbit  {Plate  II.  Fig.  6.)  to  be  eleva- 
ted above  the  plane  of  the  paper,  or  earth's  orbit,  it  is  evident 
that  the  earth's  shadow,  at  full  moon,  would  fall  below  the  moon ; 
the  left-hand  part  of  the  moon's  orbit  at  the  same  time  would  be 
depressed  below  the  plane  of  the  paper,  and  the  shadow  of  the 
moon,  at  the  time  of  new  moon,  would  fall  below  the  earth.  In 
this  case  the  moon's  nodes  would  be  between  e  and  a,  and  between 
G  and  h,  and  there  would  be  no  eclipse,  either  at  the  full  or  new 
moon  ;  but  if  the  part  of  the  moon's  orbit  between  g  and  h  be  ele- 
vated above  the  plane  of  the  paper,  or  earth's  orbit ;  the  part  be- 
tween E  and  a  will  be  depressed,  the  line  of  the  moon's  nodes  will 
then  pass  through  the  centre  of  the  earth  and  that  of  the  moon, 
and  an  eclipse  will  ensue.f  An  eclipse  of  the  sun  begins  on  the 
western  side  of  his  disc,  and  ends  on  the  eastern ;  and  an  eclipse 
of  the  moon  begins  on  the  eastern  side  of  her  disc,  and  ends  on 
the  western. 


*  Emerson's  Astronomy,  sect.  7.  page  339. 

t  If  you  draw  the  figure  on  card-paper,  and  cut  out  the  moon,  her  shadow  and 
orbit,  so  as  turn  on  the  hne  a  e  g  6,  &c.  the  above  illustration  will  be  rendered 
more  familiar. 

22 


170  ON  SOLAR  AND  LUNAR  ECLIPSES.  Part  XL 

Number  of  Eclipses  in  a  Year. 

*  The  average  number  of  eclipses  in  a  year  is  fow%  two  of  the 
sun  and  two  of  the  moon ;  and  as  the  sun  and  moon  are  as  long 
below  the  horizon  of  any  particular  place  as  they  are  above  it,  the 
average  number  of  visible  eclipses  in  a  year  is  two,  one  of  the 
sun  and  one  of  the  moon ;  the  lunar  eclipse  fi^equently  happens 
a  fortnight  after  the  solar  one,  or  the  solar  one  a  fortnight  after 
the  lunar  one. 

The  most  general  number  of  eclipses,  in  any  year,  is  four ;  there 
are  sometimes  six  eclipses  in  a  year,  hut  there  cannot  he  more  than 
seven,  nor  fewer  than  two. 

The  reason  will  appear,  by  considering  that  the  sun  can  not 
pass  both  the  nodes  of  the  moon's  orbit  more  than  once  a:year, 
making  four  eclipses,  except  he  pass  one  of  them  in  the  beginning 
of  the  year ;  in  this  case  he  may  pass  the  same  node  again  a  little 
before  the  end  of  the  year,  because  he  is  about  173*  days  in  pass- 
ing from  one  node  to  the  other ;  therefore  he  may  return  to  the 
same  node  in  about  346  days,  which  is  less  than  a  year,  making 
six  eclipses.  As  twelve  lunationsf ,  or  354  days  from  the  eclipse 
in  the  beginning  of  the  year  may  produce  a  new  moon  before 
the  year  is  ended,  which  (on  account  of  the  retrograde  motion  of 
the  moon's  node)  may  fall  within  the  solar  hmit,  it  is  possible  for 
seven  eclipses  to  happen  in  a  year,  five  of  the  sun  and  two  of  the 
moon.  When  the  moon  changes  in  either  node,  she  cannot  be 
near  enough  to  the  other  node  at  the  time  of  the  next  full  moon 
to  be  eclipsed,  and  in  six  lunar  months  afterwards,  or  about  177 
days,  she  will  change  near  the  other  node  ;  in  this  case  there  can 
not  be  more  than  two  eclipses  in  a  year,  and  both  of  the  sun. 

The  ecliptic  limits  of  the  sun  are  greater  than  those  of  the 
moon,  and  hence  there  will  be  more  solar  than  lunar  eclipses,  in 
the  ratio  of  17°  2r  to  IT  34',  or  nearly  of  3  to  2  ;  but  more  lunar 
than  soTar  eclipses  are  seen  at  any  given  place,  because  a  lunar 
eclipse  is  visible  to  a  whole  hemisphere  at  once,  whereas  a  solar 
eclipse  is  visible  only  to  a  part,  as  has  been  observed  before,  and 
therefore  there  is  a  greater  probability  of  seeing  a  lunar  than  a 
solar  eclipse. 


*  The  moon's  nodes  have  a  retrograde  motion  of  about  19 J  degrees  in  a  year 

(seepage  147),  therefore  the  sun  M'ill  have  to  move  (180  =)  170|  degrees 

2 

from  one  node  to  the  other.  But  it  has  been  shown  in  a  preceding  note,  (see  page 
36,)  that  the  sun's  apparent  diurnal  motion  is  about  59'  in  a  day ;  hence  59'  :  1  day 
:  :  170J°  :  173  days. 

t  That  is,  12  times  29  days  12  hours  44  min.  3  sec,  or  354  days  8  hours  48  min. 
36  sec. 


Chap,  VII. 


OF  THE  CALENDAR. 


171 


CHAPTER  Vli. 

Of  the  Calendar. 

The  Calendar  is  a  distribution  of  time,  as  accommodated  to 
the  various  uses  of  life,  and  contains  the  division  of  the  year  into 
months,  weeks,  days,  &c.  distinguishing  the  several  festivals,  and 
other  remarkable  days.  The  manner  of  reckoning  time  now  in 
use  was  instituted  by  Pope  Gregory  in  1582,  and  adopted  in  Eng- 
land in  1752. 

The  Common  Notes  for  the  year,  usually  given  in  the  almanacs, 
are,  The  Cycle  of  the  Moon,  or  Golden  Number  ;  the  Epact;  the 
Cycle  of  the  Sun  and  the  Dominical  Letter;  the  number  of  Direc- 
tion ;  and  the  Roman  Indiction.* 

I.  The  Cycle  of  the  Moon  is  a  period  of  19  years,  after  which 
the  new  and  full  moons  fall  on  the  same  day  of  the  month  as  they 
did  at  the  beginning  of  the  period.  Any  number  of  this  period  is 
called  the  Golden  Number. 

To  find  the  Golden  Number  for  any  Year. 

Rule.  Add  1  to  the  given  year,  and  divide  the  sum  by  19,  the 
remainder  is  the  Golden  Number.  If  there  be  no  remainder,  the 
Golden  Number  is  19, 

Example.  What  is  the  Golden  Number  for  the  year  1825  ? 

(1825+ 1)  19  leaves  a  remainder  of  2,  which  therefore  is  the 
Golden  Number. 

II.  The  Epact  for  any  year  is  the  moon's  age  at  the  beginning 
of  that  year;  that  is,  the  number  of  days  which  have  elapsed  since 
the  last  new  moon  in  the  preceding  year.i  Its  use  is  to  find  the 
Paschal  full  moon. 

To  find  the  Epact  for  any  Year  till  1900. 

Rule.  Find  the  Golden  Number  and  subtract  1  from  it,  mul- 
tiply the  remainder  by  11,  and  the  product  will  be  the  Epact;  if 


*  The  Roman  Indiction  is  of  no  use  whatever  in  the  Calendar.  It  waa  a  period 
of  15  years,  in  which  the  Romans  collected  a  tax  from  the  countries  which  they 
had  conquered.  To  find  the  Roman  Indiction  add  3  to  the  year  of  Christ,  and 
divide  the  sum  by  15,  the  remainder  is  the  Indiction.  Thus,  the  indiction  for  1825 
is  13,  for  (1825  +3)  -r-  15  leaves  a  remainder  of  13. 

The  Julian  Period  appears  in  the  Nautical  Almanic  for  1825 ;  it  is  of  no  use  in 
the  calendar ;  however  it  may  be  found  by  adding  4713  to  the  year  of  Christ.  Thus, 
1825-1-4713  =  6538  the  year  of  the  Juhan  Period. 


m 


OF  THE  CALENDAR. 


Part  IL 


the  product  exceed  30,  divide  it  by  30,  and  the  remainder  will 
be  the  Epact.    When  the  golden  number  is  1,  the  Epact  is  29. 
Example,    What  is  the  epact  for  the  year  1825  1 
The  Golden  Number  (already  found)  is  2,  hence  (2 — 1  xH) 
=11,  which  is  the  Epact. 

The  Epact  for  1824  is  29,  the  Golden  Number  being  1. 


A  Table  of  the  Epacts  till  the  Year  1900. 


Golden 
Numbers, 

Epacts. 

Golden 
Numbers. 

_  Epacts. 

Golden 
Numbers. 

Epacts. 

Golden 
Numbers. 

Epacts. 

1 

XXIX. 

6 

XXV. 

il 

XX. 

16 

XV. 

2 

XI. 

7 

VI. 

12 

I. 

17 

XXVI. 

3 

XXII. 

S 

XVII. 

13 

XII. 

18 

VII. 

4 

III. 

9 

XXVIII. 

14 

XXIII. 

19 

XVIII. 

5 

XIV. 

10 

IX. 

15 

IV. 

III.  The  Cycle  of  the  Sun  is  a  period  of  28  years,  after  which 
the  days  of  the  month  return  to  the  same  days  of  the  week.  This 
cycle  has  no  reference  to  the  apparent  motion  of  the  sun,  its  chief 
use  being  to  find  the  Dominical  Letter. 

In  order  to  connect  the  days  of  the  week  with  the  days  of  the 
year,  the  first  seven  letters  of  the  alphabet  are  chosen  to  mark 
the  several  days  of  the  week.  These  letters  are  arranged  in 
such  a  manner  for  every  year,  that  the  letter  a  stands  for  the  first 
of  January,  b  for  the  second,  c  for  the  third,  and  so  on.  The 
seven  letters  being  constantly  repeated  in  their  order  through  all 
the  days  of  the  year,  it*  is  plain  that  the  same  letter  will  answer 
to  Sunday  throughout  the  whole  year,  which  is  therefore  called 
the  Sunday  Letter. 

To  find  the  Cycle  of  the  Sun  for  any  Year  till  1900,  and  likewise 
the  Sunday  Letter. 

Rule.  Add  9  to  the  given  year,  and  divide  the  sum  by  28,  the 
remainder  is  the  year  of  the  solar  cycle  ;  if  there  be  no  remainder 
the  solar  cycle  is  28.  Then,  in  the  following  Table,  against  the 
solar  cycle  you  will  find  the  Dominical  Letter. 

Or,  To  the  given  year  add  its  fourth  part,  and  increase  the  sum 
by  6,  divide  the  result  by  7,  and  the  remainder  taken  from  7  leaves 
the  number  of  the  letter ;  reckoning  a  to  be  1,  b  2,  c  3,  d  4,  e  5, 


Chap.  VII. 


OP  THE  CALENDAR. 


173 


F  6,  and  g  7.  In  a  leap-year  this  rule  always  gives  the  letter 
answering  to  the  months  after  February. 


1 

ED 

5 

GF 

9 

BA 

13 

DC 

17 

FE 

21 

AG 

25 

CB 

2 

C 

6 

E 

10 

G 

14 

B 

18 

D 

22 

F 

26 

A 

3 

B 

7 

D 

11 

F 

15 

A 

19 

C 

23 

E 

27 

G 

4 

A 

8 

C 

12 

E 

16 

G 

20 

B 

24 

D 

28 

F 

In  a  leap-year  there  are  two  Sunday  letters ;  the  left-hand 
letter  is  used  till  the  end  of  February,  and  the  other  till  the  end 
of  the  vear. 

Example.  What  is  the  Dominical  Letter  for  1825?  (1825-|-9 
-i-28  leaves  a  remainder  of  14  ;  therefore  b  is  the  Sunday 

Or, *  1825+  u±±  4.6=2287,  this  divided  by  7  leaves  5.  Now 
7 — 5=2  the  number  of  the  letter,  therefore  the  letter  is  b. 

The  Sunday  Letter  for  the  year  1826  is  a. 

IV.  The  Number  of  Direction  is  a  number  to  be  added  to  the 
21st  of  March  to  show  on  what  day  of  the  month  Easter  Sunday 
falls.  The  earliest  Easter  possible  is  the  22d  of  March,  the  latest 
the  25th  of  April.  Within  these  limits  are  35  days,  and  the  num- 
ber of  direction  varies  from  1  to  35.  Thus,  if  Easter  Sunday 
fall  on  the  22d  of  March  the  number  of  direction  is  1,  if  on  the 
23d  it  is  2 ;  and  so  on  to  the  31st,  when  the  number  of  direction 
is  10.  If  Easter  Sunday  fall  on  the  first  of  April,  the  number 
of  direction  is  11,  if  on  the  2d  it  is  12,  and  so  on  to  the  25th  of 
April,  when  the  number  of  direction  is  35. 


A  Table  showing  the  number  of  Direction  for  find 

ng 

Easter  Sunday  by  the 

Golden  JSTuml 

er 

and  Do7ninical  Letter. 

G.  N. 

1  2 

i 

3 

4 

5|  6|  7 

8 

9 

10\ 

11 

12 

13 

14  15  16 

1 

17 

18 

19 

ters. 

A 

1 

26  19 

5 

26 

1233  19 

12 

26 

19 

5 

26 

12 

5  26  12 

33 

19 

12 

Q 

B 

2713 

6 

27 

133420 

13 

27 

20 

6 

27 

13 

6  20  13 

34 

20 

6 

C 

2S  14 

7 

21 

14:35121 

7 

28 

21 

7 

28 

14 

7,21  14 

28 

21 

7 

13 

o 

D 

29  15 

8 

22 

1529122 

8 

29 

15 

8 

29 

15 

1  22  15 

29 

22 

8 

'S 

E 

30  16 

2 

23 

16  30123 

9 

30 

16 

9 

23 

16 

2  23  9 

30 

23 

9 

s 

P 

2417 

3 

24 

1031124 

10 

31 

17 

10 

24 

17 

3  24' 10 

31 

17 

10 

Q  J 

2518 

4 

251,11  3218 

11 

32 

18 

4I25 

IS 

4'25'11 

32 

18 

^1 

Example.  On  what  day  of  the  month  and  in  what  month 
does  Easter  Sunday  fall  in  the  year  1825  ? 

The  Golden  number  already  found  is  2,  and  the  Sunday  Let- 
ter B.    Under  2,  and  in  a  line  with  b,  in  the  preceding  Table, 


174 


OP  THE  CALENDAR. 


Part  II. 


you  will  find  13,  which  is  the  number  of  direction.  Easier  Sun- 
day falls  therefore  on  the  3d  of  April. 

To  find  the  Paschal  Full  Moon,  and  thence  Easter  Day  by  the 


Add  six  to  the  Epact  (if  this  sum  exceed  30,  thirty  must  be 
taken  from  it,  and  subtract  the  sum  from  50,  the  remainder  is 
the  Paschal  full  moon,  or  Easter  limit.  Add  4  to  the  number  of 
the  Dominical  letter,  subtract  the  sum  from  the  limit,  and  the 
remainder  from  the  next  higher  number  which  will  divide  even 
by  7.  The  last  remainder  added  to  the  limit  will  give  the  num- 
ber of  days  from  the  first  of  March  to  Easter  Day,  both  in- 
clusive. 

Example.  Find  the  Paschal  full  moon  and  Easter  Day  for  the 
year  1825. 

The  Epact,  already  found,  is  11,  then  50— (ll-f6)=33  Easter 
limit,  or  the  Paschal  full  moon.  The  Dominical  letter  is  b,  hence 
the  number  of  the  letter  is  2 ;  and  33 — (2+4)=27,  the  next 
higher  number  to  which,  divisible  by  7,  is  28  ;  therefore  (28 — 27) 
-f  33  the  limit=34  days  from  the  first  of  March  ;  hence  Easter 
day  is  the  3d  of  April. 


A  Table  for  finding  Easter  till  the  year  1900 


Epacts. 


XXIX. 

XI. 
XXII. 

III. 

XIV. 
XXV. 
VI. 
XVII. 
XXVIII. 


Paschal  Full 
Moons. 


13  April  E. 

2  April  A. 
22  Mar.  d. 
10  April  B. 
30  Mar.  e. 
18  April  c. 

7  April  F. 
27  Mar.  b. 
15  April  G. 


Epacts. 


IX. 
XX. 

I. 

XII. 
XXIII. 

IV. 

XV. 
XXVI. 

VII. 
XVIII. 


Paschal  Full 
Moons. 


4  April  c. 
24  Mar.  f. 
12  April  D. 

1  April  G. 
21  Mar.  c. 

9  April  A. 
29  Mar.  d. 
17  April  B. 

6  April  e. 
26  Mar.  a. 


The  use  op  the  Table.  Find  the  Epact  (by  some  of  the  pre- 
ceding methods),  against  which,  in  the  Table,  is  the  day  of  the 
Paschal  full  moon,  with  its  corresponding  weekly  letter. 

Example.    On  what  day  does  Easter  fall  in  the  year  1825  ? 

The  Epact  is  1 1 ,  against  which,  in  the  Table,  is  the  2d  of  April, 


Chap.  VII.  OF  THE  CALENDAR.  175 

the  day  of  the  Paschal  full  moon  ;  and  this  happens  on  a  Satur- 
day, as  indicated  by  the  letter  a,  b  being  the  Sunday  letter  for  the 
year  ;  hence  Easter  Day  falls  on  the  3rd  of  April. 

Having  found  Easter  Sunday,  all  the  moveable  feasts  which 
depend  upon  it  are  knovi^n. 
Septuagesima  Sunday  is  9  weeks 
Sexagesima  Sunday  is  8  weeks 

Shrove  Sunday  or  Quinquagesima  Sunday  is  7  weeks 
Shrove  Tuesday  and  Ash  Wednesday  follow  Quinquagesima 
Sunday 

Quadragesima  Sunday  is  6  weeks 
Palm  Sunday  a  week 
Good  Friday  two  days 
Low  Sunday  is  1  week 
Rogation  Sunday  is  5  weeks 

Ascension  Day  or  Holy  Thursday,  the  Thursday  following  1  c§ 
Rogation.  ?  ^ 

Whit  Sunday  is  7  weeks 
Trinity  Sunday  is  8  weeks 

Then  follow  all  the  Sundays  after  Trinity  in  order.  The  Sun- 
days between  Ash  Wednesday  and  Easter  are  called  Sundays  in 
Lent ;  and  the  Sundays  between  Easter  and  Whit  Sunday  are 
called  Sundays  after  Easter. 

V.  By  Act  of  Parliament  Easter  Day  is  the  first  Sunday  after 
the  full  moon  which  happens  upon,  or  next  after,  the  21st  of 
March ;  and  if  the  full  moon  fall  on  a  Sunday,  Easter  Day  is  the 
Sunday  After.* 


Jl 


*  The  Act  of  Parliament  does  not  refer  to  the  Astronomical  full  moon  as  deter- 
mined by  exact  calculation,  but  to  the  full  moon  as  determined  by  the  established  cal- 
endar. Thus,  in  the  year  1818,  the  astronomical  full  moon  was  on  Sunday  the  22d 
of  March,  but  the  calendar  full  moon  was  on  Saturday  the  21st,  consequently  Easter 
was  the  Sunday  following,  viz.  the  22d. 


176 


OF  THE  CALENDAR. 


Part  ih 


A  TABLE 

FOR  FINDING  THE  MOON's  AGE. 

Add  the  number  taken  from  this  table 
to  the  day  of  the  month  ;  the  sum 
(rejecting  30,  if  it  exceed  30,)  is  the 
age.   


Year. 


1823 


1824 


1825 


1826 


1827 


1828 


1829 


1830 


1831 


1832 


1833 


1834 


1835 


1836 


1837 


1838 


1839 
1840 
1841 


14  15 


25i26 

e!  7 


17jl8 
28'29 
9110 


23 


28  28 


17 


Days. 


High  Water 


H.  M. 


0 

0 

0 

1 

U 

ob 

2 

1 

11 

3 

1 

46 

4 

2 

21 

5 

3 

1 

6 

3 

44 

7 

4 

37 

8 

5 

40 

9 

6 

58 

10 

8 

14 

11 

9 

17 

12 

10 

9 

13 

10 

53 

14 

11 

33 

15 

12 

8 

16 

12 

45 

17 

13 

19 

18 

13 

54 

19 

14 

30 

20 

15 

11 

21 

15 

56 

22 

16 

51 

23 

18 

0 

24 

19 

18 

25 

20 

31 

26 

21 

31 

27 

22 

21 

28 

23 

3 

29 

23 

42 

29^ 

24 

0 

The  use  op  the  Table.  To  find  the  time  of  new  moon.  Subtract  the  number 
in  the  Table,  opposite  to  the  given  year,  and  under  the  given  month,  from  30. 

Examples.  The  time  of  new  moon  in  February,  1825,  is  on  the  17th  (=30-  13)  ; 
and  so  on  for  any  other  year  or  month. 

To  find  the  time  of  full  moon.  Subtract  the  number  in  the  Table,  opposite  to 
the  given  year,  and  under  the  given  month,  from  30 ;  if  the  remainder  be  15, 


Chap.  VII. 


OF  THE  CALENDAR. 


177 


full  moon  happens  on  the  30th  day  of  the  month  ;  if  the  remainder  exceed  15,  the 
the  excess  above  15  is  the  day  of  tlie  irionth  on  which  full  moon  happens;  if  ihe 
•  remainder  fall  short  of  1 5,  add  15  to  it,  and  the  sum  will  show  the  day  of  the  month 
on  which  full  irioon  v\  ill  happen. 

Examples.  Full  moon  hu[)p('ns  on  June  30th,  1S25,  for  30 — 15=15.  In  .Janu- 
ary, 1825,  full  moon  falls  on  ihe4ih,  for  30  — ll  =  19,and  19  —  15=4.  In  July  1825, 
full  moon  falls  on  the  29lh,  for  30—18=14,  and  14 -f  15=29. 

N.  B.  ThouiJ  1  the  pr.iceding  table  be  calculated  only  for  19  years,  it  will  answer 
till  the  year  1900,  by  changing  ihe  years  at  the  expiration  of  19.  'fhus  instead  of 
1823,  write  1342,  and  so  on  m  a  gradual  sue  ession  to  1S60,  without  any  alteration 
of  the  figures  under  the  months;  and  when  these  years  are  elapsed,  begin  again 
with  1861,  &c.  The  column  m  the  preceding  Table  under  January,  shows  the 
Epacts  for  the  respective  years  prefixed  ;  and  the  right-hand  column  annexed  to 
the  moon's  age  is  used  m  finding  the  time  of  high  water,  in  the  succeeding  prob- 
lems. 

VI.  Of  the  Year  hy  the  Gregorian  Account. 

The  year,  according  to  our  present  mode  of  reckoning,  con- 
sists of  365  days  for  three  years  together,  and  every  fourth  year 
consists  of  366  da^s,  which  is  called  a  leap-year,  in  which  the 
nnonth  of  February  has  29  d  lys.  But  the  centuries  which  will 
not  divide  even  by  4,  such  as  1700,1800, 1900,  are  not  leap  year^ ; 
2000  is  a  leap-year,  because  20  centuries  are  divisible  by  4  :  2100, 
2200,  2300,  are  not  leap  years,  and  so  on  for  succeeding  cen- 
turies. 

Let  us  examine  the  accuracy  of  this.  By  making  every  fourth 
year  a  leap-year  the  average  length  of  each  year  is  365^  days  or 
365  days  6  hours  ;  now  the  solar  year  consists  of  365  days  5  hours 
48  minutes,  48  seconds  {Def.  62),  the  diiference  is  11  minutes 
12  seconds  in  1  year,  or  3  days  2  hours  40  minutes  in  400  years  ; 
but  the  Gregorian  mode  of  reckoning  provides  for  the  3  days,  by 
rejecting  the  intercalary  day  in  the  centuries  which  are  not  di- 
visible by  4,  as  17,  18,  19,  &;c.  hence  the  error  in  the  Gregorian 
calendar  is  2  hours  40  minutes  in  400  years,  or  one  day  in  3600 
years  :  an  error  which  the  present  generation  need  not  trouble 
themselves  about  correcting.  To  this  we  may  add  that  the 
greatest  practical  astronomers  have  not  agreed  definitively  oa  the 
exact  length  of  the  solar  or  tropical  year. 

D.  H.  M.  S. 

According  to  Maj^er,  this  year  is     .       .       365  5  48  42i 
Lalande,  .       .       .       365  5  48  48 

Baron  de  Zach,        .       .       365  5  48  50.9 
Delambre,        .       .       .       365  5  48  51.6 
From  the  variety  in  these  numbers,  which  are  of  the  highest 
authority,  it  is  manifest  that  the  precise  error  of  the  Gregorian 
calendar  is  not  easy  to  be  determined. 

33 


PART  III. 


CONTAINING   PROBLEMS   PERFORMED    BY  THE    TERRESTRIAL  AND 
CELESTIAL  GLOBES. 


CHAPTER  I. 

Problems  performed  by  the  Terrestrial  Globe, 

PROBLEM  1. 

To  find  the  latitude  of  any  given  place^ 

Rule.  Bring  the  given  place  to  that  part  of  the  brass  me- 
ridian which  is  numbered  from  the  equator  towards  the  poles : 
the  degree  above  the  place  is  the  latitude.  If  the  place  be  on 
the  north  side  of  the  equator,  the  latitude  is  north ;  if  it  be  on  the 
south  side  the  latitude  is  south. 

On  small  globes  the  latitude  of  a  place  cannot  be  found  nearer  than  to  about  a 
quarter  of  a  degree.  Each  degree  of  the  brass  meridian  on  the  largest  globes  is 
generally  divided  into  three  equal  parts,  each  part  containing  twenty  geographical 
miles  ;  on  such  globes  the  latitude  may  be  found  to  10'. 

Examples.    What  is  the  latitude  of  Edinburgh  ? 

Answer.    56o  north. 

2.  Required  the  latitudes  of  the  following  places  : 


Amsterdam  Florence  Philadelphia 

Archangel  Gibraltar  Quebec 

Barcelona  Hamhurgh  Rio  Janeiro 

Batavia  Ispahan  Stockholm 

Bencoolen  Lausanne  Turin 

Berlin  Lisbon  Vienna 

Cadiz  Madras  Warsaw 

Canton  Madrid  Wilna 

Dantzic  Naples  Washington 

Drontheim  Paris  York. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


179 


3.  Find  all  the  places  on  the  globe  which  have  no  latitude. 

4.  What  is  the  greatest  latitude  a  place  can  have  ? 

PROBLEM  II. 

To  find  all  those  places  which  have  the  same  latitude  as  any 
given  place. 

Rule.  Bring  the  given  place  to  that  part  of  the  brass  meridian 
w^hich  is  numbered  from  the  equator  towards  the  poles,  and  ob- 
serve its  latitude ;  turn  the  globe  round,  and  all  places  passing 
under  the  observed  latitude  are  those  required. 

All  places  in  the  same  latitude  have  the  same  length  of  day  and  night,  and  the 
same  seasons  of  the  year,  though  from  local  circumstances,  they  may  not  have 
the  same  atmospherical  temperature.    See  the  note,  page  38. 

Examples.  1.  What  places  have  the  same,  or  nearly  the 
same  latitude  as  Madrid  ? 

Answer.  Minorca,  Naples,  Constantinople,  Samarcand,  Philadelphia,  Pe- 
kin  &c. 

2.  What  inhabitants  of  the  earth  have  the  same  length  of  days 
as  the  inhabitants  of  Edinburgh  ? 

3.  What  places  have  nearly  the  same  latitude  as  London  ? 

4.  What  inhabitants  of  the  earth  have  the  same  seasons  of  the 
year  as  those  of  Ispahan  ? 

5.  Find  all  places  of  the  earth  which  have  the  longest  day  the 
same  length  as  at  Port  Royal  in  Jamaica. 

PROBLEM  III. 

To  find  the  longitude  of  any  place. 

Rule.  Bring  the  given  place  to  the  brass  meridian,  the  num- 
ber of  degrees  on  the  equator,  reckoning  from  the  meridian  pass- 
ing through  London  to  the  brass  meridian,  is  the  longitude.  If 
the  place  lie  to  the  right  hand  of  the  meridian  passing  through 
London,  the  longitude  is  east ;  if  to  the  left  hand,  the  longitude  is 
west. 

On  Adam's  and  Cary^s  globes  there  are  two  rows  of  figures  above  the  equator. 
When  the  place  lies  to  the  right  hand  of  the  meridian  of  London,  the  longitude 
must  be  counted  on  the  upper  line ;  when  it  lies  to  the  left  hand  it  must  be  counted 
on  the  lower  hne.  Bardin's  New  British  Globes  have  also  two  rows  of  figures 
above  the  equator,  but  the  lower  line  is  always  used  in  reckoning  the  longi- 
tude. 


180 


PROBLEMS  PERFORMED  BY 


Part  III. 


Examples.    1.  What  is  the  longitude  of  Petersburg  ? 

Answer.    30|°  east. 

2.  What  is  the  longitude  of  Philadelphia  ? 

Ansioer.    75,|°  west. 

3.  Required  the  longitudes  of  the  following  places  : 


Aberdeen 

Alexandria 

Barbadoes 

Bombay 

Botany  Bay 

Canton 

Carlscrona 

Cayenne 


Civita  Vecchia 

Constantinople 

Copenhagen 

Drontheim 

Ephesus 

Gibraltar 

Leghorn 

Liverpool 


Lisbon 

Madras 

Masulipatam 

Mecca 

Nankin 

Palermo 

Pondicherry 

Queda. 


4.  What  is  the  greatest  longitude  a  place  can  have 


PROBLEM  IV. 

To  find  all  those  places  that  have  the  same  longitude  as  a 
given  place. 

Rule.  Bring  the  given  place  to  the  brass  meridian,  then  all 
places  under  the  same  edge  of  the  meridian  from  pole  to  pole 
have  the  same  longitude. 

All  people  situated  under  the  same  meridian  from  66°  28'  north  latitude  to  66° 
28'  south  latitude,  have  noon  at  the  sane  time;  or,  if  it  be  one,  two,  three,  or  any 
number  of  hours  before  or  after  noon  with  one  particular  place,  it  will  be  the  same 
hour  with  every  other  place  situated  under  the  same  meridian. 

Examples.  I.  What  places  have  the  same,  or  nearly  the  same 
longitude  as  Stockholm  ? 

Answer.    Dantzic,  Presburg,  Tarento,  the  Cape  of  Good  Hope,  &c. 

2.  What  places  have  the  same  longitude  as  Alexandria? 

3.  When  it  is  ten  o'clock  in  the  evening  at  London,  what  in- 
habitants of  the  earth  have  the  same  hour? 

4.  What  inhabitants  of  the  earth  have  midnight  when  the  in- 
habitants of  Jamaica  have  midnight? 

5.  What  places  of  the  earth  have  the  same  longitude  as  the  fol- 
lewing  places? 

London  Quebec  The  Sandwich -islands 

Pekin  Dublin  Pelew  islands. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


181 


PROBLEM  V. 

To  find  the  latitude  and  longitude  of  any  place. 

Rule.  Bring  the  given  place  to  that  part  of  the  brass  meridi- 
an which  is  numbered  from  the  equator  towards  the  poles ;  the 
degree  above  the  place  is  the  latitude,  and  the  degree  on  the 
equator,  cut  by  the  brass  meridian,  is  the  longitude. 

This  problem  is  only  an  exercise  of  ihe  first  and  third. 

Examples.  1.  What  are  the  latitude  and  longitude  of  Peters- 
burg ? 

Answer.    Latitude  60°  N.  longitude  30J«>  E. 

2.  Required  the  latitudes  and  longitudes  of  the  following 


places : 

Acapulco  Cusco  Lima 

Aleppo  Copenhagen  Lizard 

Algiers  Durazzo  Lubec 

Archangel  Elsinore  Malacca 

Belfast  Flushing  Manilla 

Bergen  Cape  Guardafui  Medina 

Buenos  Ayres      Hamburgh  Mexico 

Calcutta  Jeddo  Mocha 

Candy  Jaffa  Moscow 

Corinth  Ivica  Oporto 


PROBLEM  VL 

To  find  any  place  on  the  globe,  having  the  latitude  and  longitude 
of  that  place  given. 

Rule.  Find  the  longitude  of  the  given  place  on  the  equator, 
and  bring  it  to  that  part  of  the  brass  meridian  which  is  numbered 
from  the  equator  towards  the  poles :  then  under  the  given  lati- 
tude, on  the  brass  meridian,  you  will  find  the  place  required. 

Examples.  L  What  place  has  151^°  east  longitude,  and  34" 
south  latitude  ? 

Answtr.   Botany  Bay. 


182 


PROBLEMS  PERFORMED  BY 


Part  111. 


2.  What  places  have  the  following  latitudes  and  longitudes 


Latitudes. 

Longitudes. 

Latitudes. 

Lon 

gitudes. 

50° 

6'  N. 

5° 

54  W. 

19° 

26'  N. 

100° 

6  W. 

48 

12  N. 

16 

16  E. 

59 

56  N. 

30 

19  E. 

55 

58  N. 

3 

12  W. 

0 

13  S. 

78 

55  W. 

99  N 

A 

«-»!  Xli. 

69 

53  W. 

31 

13  N. 

29 

55  E. 

59 

21  N. 

1  o 

18 

4  E. 

64 

34  N. 

38 

58  E. 

8 

32  N. 

81 

11  E. 

34 

29  S. 

18 

23  E. 

5 

9  S. 

119 

49  E. 

3 

49  S. 

102 

10  E. 

22 

54  S. 

42 

44  W. 

34 

35  S. 

58 

31  W. 

36 

5  N.  - 

5 

22  W. 

32 

25  N. 

52 

50  E. 

32 

38  N. 

17 

6  W. 

PROBLEM  VII. 

To  find  the  difference  of  latitude  between  any  two  places. 

Rule.  Bring  one  of  the  places  to  that  half  of  the  brass  merid- 
ian which  is  numbered  from  the  equator  towards  the  poles,  and 
mark  the  degree  above  it ;  then  bring  the  other  place  to  the  me- 
ridian, and  the  number  of  degrees  between  it  and  the  above  mark 
will  be  the  difference  of  latitude. 

Or,  Find  the  latitudes  of  both  the  places  (by  Prob.  I.)  then,  if 
the  latitude  be  both  north  or  both  south,  substract  the  less  latitude 
from  the  greater,  and  the  remainder  will  be  the  difference  of  lat- 
itude ;  but,  if  the  latitudes  be  one  north  and  the  other  south,  add 
them  together,  and  their  sum  will  be  the  difference  of  latitude. 

Examples.  1.  What  is  the  difference  of  latitude  between 
Philadelphia  and  Petersburg  ? 

.Answer.    20  degrees. 

2.  What  is  the  difference  of  latitude  between  Madrid  and 
Buenos  Ayres  ? 

.Answer.    75  degrees. 

3.  Required  the  difference  of  latitude  between  the  following 
places  : 


London  and  Rome 
Delhi  and  Cape  Comorin 
Vera  Cruz  and  Cape  Horn 
Mexico  and  Botany  Bay 
Astracan  and  Bombay 
St.  Helena  and  Manilla 
Copenhagen  and  Toulon 
Brest  and  Inverness 
Cadiz  and  Sierra  Leone 


Alexandria  and  the  Cape  of 

Good  Hope 
Pekin  and  Lima 
St.  Salvadore  and  Surinam 
Washington  and  Quebec 
Porto  Bello  and  the  Straits  of 

Magellan 
Trinidad  I.  and  Trincomale 
Bencoolen  and  Calcutta. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


183 


4.  What  two  places  on  the  globe  have  the  greatest  difference 
of  latitude  ? 


PROBLEM  VIII. 

To  find  the  difference  of  longitude  between  any  two  places. 

Rule.  Bring  one  of  the  given  places  to  the  brass  meridian, 
and  mark  its  longitude  on  the  equator ;  then  bring  the  other  place 
to  the  brass  meridian,  and  the  number  of  degrees  between  its 
longitude  and  the  above  mark,  counted  on  the  equator,  the  near- 
est way  round  the  globe,  will  show  the  difference  of  longitude. 

Or,  find  the  longitudes  of  both  the  places  (by  Prob.  III.)  then, 
if  the  longitudes  be  both  east  or  both  west,  subtract  the  less  longi- 
tude from  the  greater,  and  the  remainder  will  be  the  difference 
of  longitude  ;  but,  if  the  longitudes  be  one  east  and  the  other  west, 
add  them  together,  and  their  sum  will  be  the  difference  of  longi- 
tude. 

When  this  sum  exceeds  180  degrees,  take  it  from  360,  and  the 
remainder  will  be  the  difference  of  longitude. 

Examples.  1.  What  is  the  difference  of  longitude  between 
Barbadoes  and  Cape  Verd  ? 

Answer.    43o  42'. 

2.  What  is  the  difference  of  longitude  between  Buenos  Ayres 
and  the  Cape  of  Good  Hope  ? 

Answer.    76°  54'. 

3.  What  is  the  difference  of  longitude  between  Botany  Bay 
and  O'why'ee  ? 

Answer.    52°  45',  or  52|  degrees. 

4.  Required  the  difference  of  longitude  between  the  following 
places : 

Vera  Cruz  and  Canton 
Bergen  and  Bombay 
Columbo  and  Mexico 
Juan  Fernandes  I.  and  Manil- 
la. 

Pelew  I.  and  Ispahan. 
Boston  in  America  and  Berlin 


Constantinople  and  Batavia 
Bermudas  I.  and  I.  of  Rhodes 
Port  Patrick  and  Berne 
Mount  Heckla  and  Mount  Ve- 
suvius 

Mount  iEtna  and  Teneriffe 
North  Cape  and  Gibraltar. 

5.  What  is  the  greatest  difference  of  longitude  comprehended 
between  two  places  ? 


184 


PROBLEMS  PERFORMED  BY 


Part  III. 


PROBLEM  IX. 


To  find  the  distance  between  any  two  places. 

Rule.  The  shortest  distance  between  any  two  places  on  the 
earth,  is  an  arc  of  a  great  circle  contained  between  the  two  pla- 
ces. Therefore,  lay  the  graduated  edge  of  the  quadrant  of  alti- 
tude over  the  two  places,  so  that  the  division  marked  o  may  be  on 
one  of  the  places,  the  degrees  on  the  quadrant  comprehended  be- 
tween the  two  places  will  give  their  distance;  and  if  these  degrees 
be  multiplied  by  60,  the  product  will  give  the  distance  in  geo- 
graphical miles;  or  multiply  the  degrees  by  69.1,  and  the  pro- 
duct will  give  the  distance  in  English  miles. 

Or,  take  the  distance  between  the  two  places  with  a  pair  of 
compasses,  and  apply  that  distance  to  the  equator,  which  will 
show  how  many  degrees  it  contains. 

If  the  distance  between  the  two  places  should  exceed  the  length 
of  the  quadrant,  stretch  a  piece  of  thread  over  the  two  places, 
and  mark  their  distance  ;  the  extent  of  thread  between  these 
marks,  applied  to  the  equator,  from  the  meridian  of  London,  will 
show  the  number  of  degrees  between  the  two  places. 

Examples.  1.  What  is  the  nearest  distance  between  the  Liz- 
ard and  the  island  of  Bermudas  ? 


45|  distance  in  degrees. 
60 


2700 
30 
15 


2745  geographical  miles. 


45.5 
69.1 

455 
4095 
2730 


3144.05  English  miles. 


2.  What  is  the  nearest  distance  between  the  island  of  Bermu- 
das and  St.  Helena  ? 


73^  distance  in  degrees. 
60 


4380 
30 


4410  geographical  miles. 


73.5 
69.1 

735 
6615 
4410 


5078.85  English  miles. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


185 


3.  What  is  the  nearest  distance  between  London  and  Botany 
Bay? 

154 
69.1 


154 
1386 
924 

10641.4  English  miles. 

4.  What  is  the  direct  distance  between  London  and  Jamaica, 
in  geographical  and  English  miles  ? 

5.  What  is  the  extent  of  Europe  in  English  miles,  from  Cape 
Matapan  in  the  Morea,  to  the  North  Cape  in  Lapland  ? 

6.  What  is  the  extent  of  Africa  from  Cape  Verd  to  Cape 
Guardafui  ? 

7.  What  is  the  extent  of  South  America  from  Cape  Blanco  in 
the  west  to  Cape  St.  Roque  in  the  east  ? 

8.  Suppose  the  track  of  a  ship  to  Madras  be  from  the  Lizard  to 
St.  Anthony,  one  of  the  Cape  Verd  islands,  thence  to  St.  Helena, 
thence  to  the  Cape  of  Good  Hope,  thence  to  the  east  of  the  Mau- 
ritius, thence  a  little  to  the  south  east  of  Ceylon,  and  thence  to 
Madras ;  how  many  English  miles  is  the  Land's  end  from  Madras? 


60 


9240  geographical  miles. 


Simple  as  the  preceding  problem  may  appear  in  theory,  on  a  superficial  view,  yet 
when  applied  to  practice,  the  difficulties  which  occur  are  almost  insuperable.  In 
sailing  across  the  trackless  ocean,  or  travelling  through  extensive  and  unknown 
countries,  our  only  guide  is  the  compass,  and  except  two  places  be  situated  direct- 
ly north  and  south  of  each  other,  or  upon  the  equator,  though  we  may  travel  or 
sail  from  one  place  to  the  other  by  the  compass,  yet  we  can  not  take  the  shortest 
route,  as  measured  by  the  quadrant  of  altitude. 

To  illustrate  these  observations  by  examples:  first,  Let  two  places  be  situated 
in  latitude  50^  north,  and  differing  in  longitude  48 '  50',  which  will  nearly  corres- 
pond with  the  Land's  End  and  the  eastern  coast  of  Newfoundland.  The  arc  of 
nearest  distance  being  that  of  a  great  circle,  truly  calculated  by  spherical  trigonometry, 
is  30^  49'  equal  to  1849_i_  geographical  miles,  or  2141|,  English  miles  j  but,  if 
a  ship  steer  from  the  Land's  End  directly  westward,  in  the  latitude  of  50'  north, 
till  her  difference  of  longitude  be  48'  50',  her  true  distance  sailed  will  be  18832  ge- 
ographical miles,  or  2181^  Enghsh  miles,  making  a  circuitous  course  of  34_3_  ge- 
ographical miles,  or  40|  English  miles.  Those  who  are  acquainted  with  spherical 
trigonometry  and  the  principles  of  navigation,  particularly  great  circle  sailing  know 
that  it  is  impossible  to  conduct  a  ship  exactly  on  the  arc  of  a  great  circle,  except,  as 
before  observed,  on  the  equator  or  meridian ;  for,  in  this  example,  she  must  be 
steered  through  all  the  different  angles,  from  n.  70°  49'  30''  w.  to  90  degrees,  and 
continue  sailing  from  thence  through  all  the  same  varieties  of  angles,  till  she  ar- 
rives at  the  intended  place,  where  the  angle  will  become  70'  49'  3^',  the  same  as 
at  first. 

Secondly.  Suppose  it  were  required  to  find  the  shortest  distance  between  the 
Lizard,  lat.  49'  57'  n.  long.  5°  21'  w.  and  the  island  of  Bermudas,  lat.  32'  35'  n  ; 
long.  63^  32'  w.  The  arc  of  a  great  circle  contained  between  the  two  places  will 
be  found,  by  spherical  trigonometry,  to  be  45^  44',  being  2744  geographical  miles, 

24 


186 


PROBLEMS  PERFORMED  BY 


Part  IIL 


or  3178  English  miles.  See  the  method  of  calculating  such  problems  in  Keith's 
Trigonometrif,  fourth  edition,  page  313.  Now  for  a  ship  to  run  this  shortest  track, 
she  must  sail  from  the  Lizard  s.  89^  29'  w.  and  gradually  lessen  her  course  so  as  to 
arrive  at  Bermudas  on  the  rhumb  bearing  s.  49  ■  47'  w. ;  but  this,  though  true  in 
theory,  is  impracticable  ;  the  course  and  distance  must  therefore  be  calculated  by 
Mercator's  Sailing.  The  direct  course  by  the  compass  will  be  found  to  be  s.  68°  9'  w, 
and  the  distance  upon  that  course  2800  geographical  miles,  or  3243  English  miles ; 
making  a  circuitous  course  of  56  geographical  miles,  or  65  EngUsh  miles. 

Hence,  to  find  the  distance  between  any  two  places  whose  latitudes  and  longitudes  are 
known,  in  order  to  travel  or  sail  from  one  place  to  the  other,  on  a  direct  course  by  the 
mariner's  compass,  the  following  methods  must  be  used  : 

1.  If  the  places  be  situated  on  the  same  meridian,  their  difference  of  latitude  will 
be  the  nearest  distance  between  them  in  degrees,  and  the  places  will  be  exactly 
north  and  south  of  each  other. 

2.  If  the  places  be  situated  on  the  equator,  their  difference  of  longitude  will  be 
the  nearest  distance  in  degrees,  and  the  places  will  be  exactly  east  and  west  of  each 
other. 

3.  If  the  places  differ  both  in  latitudes  and  longitudes,  the  distance  between 
them  and  the  point  of  the  compass  on  which  a  person  must  sail  or  travel,  from  the 
one  place  to  the  other,  must  be  found  by  Mercator^s  Sailing,  as  in  navigation. 

4.  If  the  places  be  situated  in  the  same  latitude,  they  will  be  directly  east  and 
west  of  each  other ;  and  the  difference  of  longitude,  multiplied  by  the  number  of 
miles  which  make  a  degree  in  the  given  latitude,  according  to  the  following  table, 
will  give  the  distance. 

The  following  table  is  calculated  thus :  radius  is  to  the  length  of  a  degree  upon 
the  equator,  as  the  co-sine  of  the  given  latitude  is  to  the  length  of  a  degree  in  that 
latitude.  See  this  proportion  illustrated  in  Keith's  Trigonometry,  page  296,  fourth 
edition. 


Chap.  I.  THE  TERRESTRIAL  GLOBE.  187 


ueg. 

Geog. 

English 

Geog. 

Faliah 

DpfT 

Enghsh 

T  of 

I\/T  i  1  O  C! 

T  it 

IVIiles 

]VIiles. 

T.nf 

i-icll. 

Miles. 

iviiies. 

n 
u 

no 

RQ  1  fi 

O  L 

51.43 

59.23 

61 

29.09 

f:o 
oo.ou 

1 

f;Q  QQ 

oy.uy 

32 

50.88 

58.60 

62 

9Q  1  7 

^9  44 
04.44 

z 

RQ  OR 
oy.uo 

oo 

50.32 

o  /  .y  J 

R"? 
oo 

97  94 

^1  ^7 
Ol.O/ 

o 

RQ  OT 
oy.ui 

34 

49.74 

fi7  9Q 

R4 
o'± 

9R  ^0 

.60.00 

^0  9Q 

oo.4y 

A 

59.85 

RS 

Do. yo 

^f; 
oa 

4Q  1 
'±y .  1  o 

CiR  RO 

OO.DU 

RC» 

DO 

£iO.OKi 

9Q  90 

O 

0«7.  /  / 

RQ  9.A 
03. d 

^R 
jO 

4S  f;4 

^f;  QO 
oo.yu 

RR 

DO 

94  40 

9Q  1  1 
43.1 1 

D 

Oi7.D  / 

RQ  70 
03.  /  Z 

^7 

47  Q9 
4/  .y,4 

00. ly 

R7 
0  / 

0^  44 
-00.44 

97  OR 

4/.U0 

1 

oy.oo 

oo.oo 

DO 

47  OQ 

t^A  4c; 
04.40 

ftQ 
DO 

OO  AO. 

OK  QA 

520. oy 

Q 

O 

oy 

4R  R^ 
40. DO 

7rt 

Oo.  /  If 

RO 

by 

zi.ou 

O/l  Tft 
44. /o 

y 

f;o  Oft 

;    RQ  O  K 
;  DO.^O 

4  p;  QR 

4o,yo 

KO  QQ 

05i.yo 

'70 

/u 

on  c;£j 

OQ  ftQ 
40.D0 

1  n 

oy.uy 

RQ  nc 

1  DO.UO 

'±1 

Ati  OQ 

f;o  1  f; 
OJi.lO 

71 
/  1 

1  Q  c;2 

ly.oo 

OO  CA 
44. OU 

1 1 

OO.  UU 

R*y  Q5 

o/.oo 

44.  oy 

c;  t  3  n 
01. oO 

70 

1  Q  c;/i 
10.J4 

O  1  QC 
41.00 

1  o 

oo.oy 

R*?  KQ 

o/.oy 

'±0 

4*?  Q8 
40.00 

OU-04 

7^4 
/  o 

1  7  ^A 
1  /  .04 

OO  OO 

Zv.ZU 

la 

zift 

OO  4d 

R'y 

AA 

4^  1R 
40. 10 

4Q  71 

4y.  / 1 

74 
/  4 

1R  c;/i 
1O.04 

1  Q  OC; 

ly.uo 

1 4 

R7  nt; 
D/ .uo 

49  4^i 

4Q  QR 
4O.O0 

7Ci 
/  0 

1  c; 

X  O.OO 

1  7  QQ 
1  /  .OO 

1 1; 

o '  .yo 

R7  7f^ 
O  /  .  /  o 

4R 

40 

41  RQ 
41. DO 

4Q  OO 

t:<3.UO 

7R 
/O 

1 4  c:o 
14.04 

1  R  70 
10./4 

1 A 

lo 

PA 

0 1  .Oo 

RR  49 

Do  ^.4 

47 

40  Q9 

47  1  ^ 
4/.  lo 

77 
/  / 

10. OU 

1  c;  f;4 
10.04 

1  / 

O  /  .  DO 

RR  OQ 

40  1  CI 
4U.10 

4ft  94 
4D./i4 

7Q 
/O 

1  9  47 
14.4/ 

1 A  Q7 
14. 0/ 

lO 

c;7  OR 

Rf;  79 
OD.  /  4 

4Q 
4y 

oy.oo 

4c; 

TrO.OO 

7Q 

/y 

1  1  4c: 
1  J  .40 

1  Q  1  Q 
lo.lO 

ly 

Rf?  '-id. 
OO.Ot: 

fin 

^Q  t^7 
00.0/ 

44  49 
'±4.44 

QO 
oU 

1  0  40 
1U.44 

1  O  OO 
14.UU 

90 

56.38 

51 

^7  7R 
o/ ,  /  o 

A^  4Q 

Q1 

o  1 

y.oy 

10  Q1 
J  O.Ol 

21 

56^01 

64.51 

52 

36.94 

42.54 

82 

8.35 

9.62 

22 

55.63 

64.07 

53 

36.11 

41.59 

83 

7.31 

8.42 

23 

55.23 

63.61 

54 

35.27 

40.62 

84 

6.27 

7.22 

24 

54.81 

63.13 

55 

34.41 

39.63 

86 

5.23 

6.02 

25 

54.38 

62.63 

56 

33.55 

33.64 

86 

4.19 

4.82 

26 

53.93 

62-11 

57 

32.68 

37.63 

87 

3.14 

3.62 

27 

53.46 

61.57 

58 

31.80 

36.62 

88 

2.09 

2.41 

28 

52.98 

61.01 

59 

30.90 

35.59 

89 

1.05 

1.21 

29 

52.48 

60.44 

60 

30.00 

34.55 

90 

0.00 

0.00 

30 

51.96 

59.84 

Length  of  a  degree 

69.1  English  miles. 

PROBLEM  X. 

A  place  being  given  on  the  globe,  to  find  all  places,  which  are  situa- 
ted at  the  same  distance  from  it  as  any  other  given  place. 

Rule.  Lay  the  graduated  edge  of  the  quadrant  of  altitude 
over  the  two  places,  so  that  the  division  marked  o  may  be  on  one 
of  the  places,  then  observe  what  degree  of  the  quadrant  stands 
over  the  other  place  ;  move  the  quadrant  entirely  round,  keeping 
the  division  marked  o  in  its  first  situation,  and  all  places  which 
pass  under  the  same  degree  which  was  observed  to  stand  over  the 
other  place,  will  be  those  sought. 

Or,  Place  one  foot  of  a  pair  of  compasses  in  one  of  the  given 
places,  and  extend  the  other  foot  to  the  other  given  place :  a  circle 


188  PROBLEMS  PERFORMED  BY  Part  III. 

described  from  the  first  place  as  a  centre,  with  this  extent,  will 
pass  through  all  the  places  sought. 

If  the  distance  between  the  two  given  places  should  exceed  the  length  of  the 
quadrant,  or  the  extent  of  a  pair  of  compasses,  stretch  a  piece  of  thread  over  the 
two  places,  as  in  the  preceding  problem. 

Examples.  1.  It  is  required  to  find  all  the  places  on  the  globe 
which  are  situated  at  the  same  distance  from  London  as  Warsaw. 

Answer.   Koningsburg,  Buda,  Posega,  AUcaiit,  &c. 

2.  What  places  are  at  the  same  distance  from  London  as  Pe- 
tersburgh  ? 

3.  What  places  are  at  the  same  distance  from  London  as  Con- 
stantinople ? 

4.  What  places  are  at  the  same  distance  from  Rome  as  Madrid? 


PROBLEM  XI. 

Given  the  latitude  of  a  place  and  its  distance  from  a  given  place,  to 
find  that  place  whereof  the  latitude  is  given. 

Rule.  If  the  distance  be  given  in  English  or  geographical 
miles,  turn  them  into  degrees  by  dividing  by  69|  for  English  miles, 
or  60  for  geographical  miles  ;  then  put  that  part  of  the  graduated 
edge  of  the  quadrant  of  altitude  which  is  marked  o  upon  the  given 
place,  and  move  the  other  end  eastward  or  westward  (according 
as  the  required  place  lies  to  the  east  or  west  of  the  given  place,) 
till  the  degrees  of  distance  cut  the  given  parallel  of  latitude : 
under  the  point  of  intersection  you  will  find  the  place  sought. 

Or,  Having  reduced  the  miles  into  degrees,  take  the  same 
number  of  degrees  from  the  equator  with  a  pair  of  compasses,  and 
with  one  foot  of  the  compasses  in  the  given  place,  as  a  centre, 
and  this  extent  of  degrees,  describe  a  circle  on  the  globe  ;  turn 
the  globe  till  this  circle  falls  under  the  given  latitude  on  the  brass 
meridian,  and  you  will  find  the  place  required. 

Examples.  1.  A  place  in  latitude  60°  N.  is  i320|  English 
miles  from  London,  and  it  is  situated  in  E.  longitude  ;  required 
the  place. 

Answer.  Divide  1320^  miles  by  69^  miles,  or,  which  is  the  same  thing,  2641 
half-miles  by  139  half-miles,  the  quotient  will  give  19  degrees;  hence  the  required 
place  is  Petersburg. 

2.  A  place  in  latitude  32^*^  N.  is  1350  geographical  miles  from 
London,  and  it  is  situated  in  W.  longitude  ;  required  the  place. 


Chap,  I. 


THE  TERRESTRIAL  GLOBE. 


189 


Answer.  Divide  1350  by  60  the  quotient  is  22^  30',  or  22  1-2  degrees ;  hence  the 
required  place  is  the  west  point  of  the  Island  of  Madeira. 

3.  What  place,  in  e.  longitude  and  41°  n.  latitude,  is  1520  Eng- 
lish miles  from  London  ? 

4.  What  place  in  w.  longitude  and  13°  n.  latitude,  is  3660  geo- 
graphical miles  from  London  1 


PROBLEM  XII. 


Given  the  longitude  of  a  place  and  its  distance  from  a  given  place, 
to  find  that  place  whereof  the  longitude  is  given. 

Rule.  If  the  distance  be  given  in  English  or  geographical 
miles,  turn  them  into  degrees  by  dividing  by  69.1  for  English  miles, 
or  60  for  geographical  miles ;  then  put  that  part  of  the  graduated 
edge  of  the  quadrant  of  altitude  which  is  marked  o  upon  the  given 
place,  and  move  the  other  end  northv\^ard  or  southward  (accord- 
ing as  the  required  place  lies  to  the  north  or  south  of  the  given 
place),  till  the  degrees  of  distance  cut  the  given  longitude  :  under 
the  point  of  intersection  you  will  find  the  place  sought. 

Or,  Having  reduced  the  miles  into  degrees,  take  the  same 
number  of  degrees  from  the  equator  with  a  pair  of  compasses, 
and  with  one  foot  of  the  compasses  in  the  given  place,  as  a  cen- 
tre, and  this  extent  of  degrees,  describe  a  circle  on  the  globe ; 
bring  the  given  longitude  to  the  brass  meridian,  and  you  will  find 
the  place,  upon  the  circle,  under  the  brass  meridian. 

Examples.  1.  A  place  in  north  latitude,  and  in  60  degrees 
west  longitude,  is  4215  English  miles  from  London ;  required 
the  place. 

.Answer.  Divide  4215  by  69.1  the  quotient  is  nearly  61  degrees;  hence  the  re- 
quired place  is  Barbadoes. 

2.  A  place  in  north  latitude,  and  in  75^  degrees  west  longitude, 
is  3120  geographical  miles  from  London  ;  what  place  is  it  ? 

3.  A  place  in  31^  degrees  east  longitude,  and  situated  south- 
ward of  London,  is  2211  English  miles  from  it;  required  the 
place. 

4.  A  place  in  29  degrees  east  longitude,  and  situated  south- 
ward of  London,  is  1520  English  miles  from  it ;  required  the 
place. 

«■ 


190 


PROBLEMS  PERFORMED  BY 


Part  III. 


PROBLEM  XIII. 

To  find  how  many  miles  make  a  degree  of  longitude  in  any  given 
parallel  of  latitude. 

Rule.  Lay  the  quadrant  of  altitude  parallel  to  the  equator, 
between  any  two  meridians  in  the  given  latitude,  which  differ  in 
longitude  15  degrees*  ;  the  number  of  degrees  intercepted  be- 
tween them  multiplied  by  4,  will  give  the  length  of  a  degree  in 
geographical  miles.  The  geographical  miles  may  be  converted 
into  English  miles  by  multiplying  by  69.1  and  dividing  by  60. 

Or,  Take  the  distance  between  two  meridians,  which  differ  in 
longitude  15  degrees  in  the  given  parallel  of  latitude,  with  a  pair 
of  compasses :  apply  this  distance  to  the  equator,  and  observe 
how  many  degrees  it  makes  :  with  which  proceed  as  above. 

Since  the  quadrant  of  altitude  will  measure  no  arc  truly  but  that  of  a  great  cir- 
cle ;  and  a  pair  of  compasses  will  only  measure  the  chord  of  an  arc,  not  the  arc 
itself  ;  it  follows  that  the  preceding  rule  cannot  be  mathematically  true,  though 
sufficiently  correct  for  practical  purposes.  When  great  exactness  is  required,  re- 
course must  be  had  to  calculation.  See  the  table  in  the  note  to  problem  IX. 
page  187. 

The  above  rule  is  founded  on  a  supposition  that  the  number  of  degrees  contained 
between  any  two  meridians,  reckoned  on  the  equator,  is  to  the  number  of  degrees 
contained  between  the  same  meridians,  on  any  parallel  of  latitude,  as  the  number 
of  geographical  miles  contained  in  one  degree  on  the  equator,  is  to  the  number  of 
geographical  miles  contained  in  one  degree  on  the  given  parallel  of  latitude.  Thus 
in  the  latitude  of  London,  two  places  which  differ  15  degrees  in  longitude,  are  9^ 
degrees  distant  by  the  rule.  Hence  15°  :  9^  :  :  60m.  :  37m.,  or  15°  :  60m.  :  :  9^  : 
37  m.,  but  15  are  to  60  as  1  to  4,  therefore,  1  :  4  :  :  9| :  37  geographical  miles 
contained  in  one  degree. 

Examples.  1.  How  many  geographical  and  English  miles 
make  a  degree  in  the  latitude  of  Pekin  ? 

Jinswer.  The  latitude  of  Pekin  is  40°  north  ;  the  distance  between  two  merid- 
ians in  that  latitude  (which  differ  in  longitude  15  degrees)  is  ll^degrees.  Now  11^ 
degrees  multipUed  by  4,  produces  46  geographical  miles  for  the  length  of  a  degree 
of  longitude,  in  the  latitude  of  Pekin  ;  and  multiplying  46  by  69.1,  and  dividing  by 
60,  the  quotient  is  52.97  English  miles. 

2.  How  many  miles  make  a  degree  in  the  parallels  of  latitude 
wherein  the  following  places  are  situated  1 

Surinam  Washington  Spitzbergen 

Barbadoes  Quebec  Cape  Verd 

Havannah  Skalholt  Alexandria 

Bermudas  North  Cape  Paris. 


♦  The  meridians  on  Cart's  large  globes  are  drawn  through  every  ten  degrees. 
The  rule  will  answer  for  these  globes,  by  reading  10  degrees  for  15  degrees,  and 
multiplying  by  6  instead  of  4. 


Chap.  L  THE  TERRESTRIAL  GLOBE.  191 


PROBLEM  XIV. 

To  find  the  hearing  of  one  place  from  another. 

Rule.  If  both  the  places  be  situated  on  the  same  parallel  of 
latitude,  their  bearing  is  either  east  or  west  from  each  other ;  if 
they  be  situated  on  the  same  meridian,  they  bear  north  and  south 
from  each  other :  if  they  be  situated  on  the  same  rhumb-line,* 
that  rhumb-line  is  their  bearing ;  if  they  be  not  situated  on  the 
same  rhumb-line,  lay  the  quadrant  of  altitude  over  the  two  places, 
and  that  rhumb-line  which  is  nearest  of  being  parrallel  to  the 
quadrant  will  be  their  bearing. 

Or,  If  the  globe  have  no  rhumb-lines  drawn  on  it,  make  a 
small  mariner's  compass  {such  as  in  Plate  I.  Fig.  4.)  and  apply 
the  centre  of  it  to  any  given  place,  so  that  the  north  and  south 
points  may  coincide  with  some  meridian ;  the  other  points  will 
show  the  bearings  of  all  the  circumjacent  places,  to  the  distance 
of  upwards  of  a  thousand  miles,  if  the  centrical  place  be  not  far 
distant  from  the  equator. 

Examples.  I.  Which  way  must  a  ship  steer  from  the  Lizard 
to  the  island  of  Bermudas  ? 

Answer.    W.  S.  W. 

2.  Which  way  must  a  ship  steer  from  the  Lizard  to  the  island 
of  Madeira  1 

Answer.    S.  S.  W. 

3.  Required  the  bearing  between  London  and  the  following 
places : 


Amsterdam  Copenhagen  Petersburg 

Athens  Dublin  Prague 

Bergen  Edinburgh  Rome 

Berlin  Lisbon  Stockholm 

Berne  Madrid  Vienna 

Brussels  Naples  Warsaw 

Buda  Paris. 


*  On  Adams'  globes  there  are  two  compasses  drawn  on  the  equator,  each  point 
of  which  may  be  called  a  rhumb-line,  being  drawn  so  as  to  cut  all  the  meridians 
in  equal  angles.  One  compass  is  drawn  on  a  vacant  place  in  the  Pacific  ocean, 
between  America  and  New-Holland ;  and  another,  in  a  similar  manner,  in  the 
Atlantic  between  Africa  and  South  America.  There  are  no  rhumb-lines  on  Gary's, 
Bardin's,  or  Addison's  globes. 


192 


PROBLEMS  PERFORMED  BY 


Part  in. 


PROBLEM  XV. 

To  find  the  angle  of  position  between  two  places. 

Rule.  Elevate  the  north  or  south  pole,  according  as  the  lati- 
tude is  north  or  south,  so  many  degrees  above  the  horizon  as  are 
equal  jto  the  latitude  of  one  of  the  given  places ;  bring  that  place 
to  the  brass  meridian,  and  screw  the  quadrant  of  altitude  upon  the 
degree  over  it ;  next  move  the  quadrant  till  its  graduated  edge 
falls  upon  the  other  place ;  then  the  number  of  degrees  on  the 
wooden  horizon,  between  the  graduated  edge  of  the  quadrant 
and  the  brass  meridian,  reckoning  towards  the  elevated  pole,  is 
the  angle  of  position  between  the  two  places. 

Examples.  1.  What  is  the  angle  of  position  between  London 
and  Prague  ? 

Answer.  90  degrees  from  the  north  towards  the  east:  the  quadrant  of  altitude 
will  fall  upon  the  east  point  of  the  horizon,  and  pass  over  or  near  the  following 
places,  viz.  Rotterdam,  Frankfort,  Cracow,  Ockzakov,  CafTa,  south  part  of  the  Cas- 
pian Sea,  Guzerat  in  India,  Madras,  and  part  of  the  island  of  Ceylon.  Hence  all 
these  places  have  the  same  angle  of  position  from  London. 

2.  What  is  the  angle  of  position  between  London  and  Port 
Royal  in  Jamaica  ? 

Answer.  90  degrees  from  the  north  towards  the  west ;  the  quadrant  of  altitude 
will  fall  upon  the  west  point  of  the  horizon. 

3.  What  is  the  angle  of  position  between  Philadelphia  and 
Madrid? 

Answer.  65  degrees  from  the  north  towards  the  east ;  the  quadrant  of  altitude 
will  fall  between  the  E.N.E.  and  N.E.  by  E.  points  of  the  horizon. 

4.  Required  the  angles  of  position  between  London  and  the 
following  places : 

Amersterdam  Copenhagen  Rome 

Berlin  Cairo  Stockholm 

Berne  Lisbon  Petersburg 

Constantinople  Madras  Quebec. 

The  preceding  problem  has  been  the  occasion  of  many  disputes  among  writers 
on  the  globes.  Some  suppose  the  angle  of  position  to  represent  the  true  bear- 
ing of  two  places,  viz.  that  point  of  the  compass  upon  which  any  person  must  con- 
stantly  sail  or  travel,  from  the  one  place  to  the  other;  while  others  contend  that 
the  angle  of  position  between  two  places  is  very  different  from  their  bearing  by 
the  mariner's  compass.  We  shall  here  endeavour  to  set  the  matter  in  a  clear 
point  of  view.  The  following  figure  represents  a  quarter  of  the  sphere,  stereo- 
graphically  projected  on  the  plane  of  the  meridian  with  the  half  meridians  and 
parallels  of  latitude  drawn  through  every  ten  degrees ;  p  represents  the  north 
pole,  and  e  q  a  portion  of  the  equator.  Now,  by  attending  to  the  manner  of 
finding  the  angle  of  position,  as  laid  down  in  the  foregoing  problem,  we  shall 


Chap,  I. 


THE  TERRESTRIAL  GLOBE. 


193 


find  that  the  quadrant  of  altitude  always  forms  the  base  of  a  spherical  tr'angle,  the  two 
sides  of  which  triangle  are  the  complements  of  the  latilides  of  the  two  p  aces,  and  the  ver- 
tical angle  is  their  difference  of  longitude.  The  angles  at  the  base  of  this  triangle 
are  the  angles  of  position  between  the  two  places. 

1.  When  the  tioo  places  are  situated  on  the  same  parallel  of  latitude. 


Let  two  places  l  and  o  be  situated  in  latitude  50'* 
north,  and  differing  in  longitude  48°  50',  which  will 
nearly  correspond  with  the  Land's  End  and  the 
eastern  coast  of  Newfoundland  {see  the  note  to  Prob. 
IX)  ;  then  op  and  lp  will  be  each  40  degrees,  the 
angle  opl,  measured  by  the  arc  w  q,  will  be  48  50' ; 
whence  the  arc  of  nearest  distance  o  n  h  may  be 
found  (by  case  Hi  page  245,  Keith's  Trigonometry) 
being  30°  39'  6",  the  angle  plo  equal  to  pol,  the 
triangle  being  isosceles,  is  70  49'  30"  ;  and  if  n  be 
the  middle  point  between  l  and  o,  the  latitude  of 
that  point  will  be  found  to  be  52°  37'  north,  and  the 
angles  p  n  l  and  p  n  o  will  be  right  angles.  Now, 
if  an  indefinite  number  of  points  be  taken  along  the 
edge  of  the  quadrant  of  altitude,  viz.  on  the  arc  l  n  o,  the  angle  of  position  between 
L  and  each  of  these  points  will  be  N.  70  40'  30  '  W. ;  but,  if  it  were  possible  for 
a  ship  to  sail  along  the  arc  l  n  o,  by  the  compass,  her  latitude  would  gradually  in- 
crease between  l  and  w,  from  50  N.  to  52  37'  N. ;  and  the  courses  she  must  steer 
would  vary  from  70  49'  30  '  at  l,  to  90°  at  n.  In  sailing  from  n  to  o,  she  must  de- 
crease her  latitude  from  52°  37'  N.  to  50°  N  and  her  courses  must  vary  from  90°, 
or  directly  west,  to  70  49'  30"  ;  but,  if  a  ship  were  to  sail  along  the  parallel  of  lat- 
itude L  m  o,  her  course  would  be  invariably  due  west.  Hence  it  follows  that,  if 
two  places  be  situated  on  the  same  parallel  of  latitude,  the  angle  of  position  be- 
tween them  cannot  represent  their  true  bearing  by  the  mariner's  compass. 

Corollary.  If  the  two  places  were  situated  on  the  equator  as  at  to  and  q,  the 
angle  of  position  between  q  and  lo,  and  between  q  and  all  the  intermediate  points, 
as  at  N,  would  be  90  degrees.  In  this  case,  therefore,  and  in  this  only,  the  angle  of 
position  shows  the  true  bearing  by  the  compass. 


2.  If  the  two  places  differ  both  in  latitudes  and  longitudes. 


Let  L  represent  a  place  in  latitude  50°  N. ;  B  a  place  in  latitude  13°  30'  N.  and 
let  their  difference  of  longitude  bpl,  measured  by  the  arc  6  q,  be  52=  58'.  The  an- 
gle of  position  between  l  and  b  (calculated  by  spherical  trigonometry)  will  be  found 
to  be  S.  68°  57'  W.  and  the  angle  of  position  between  b  and  l  will  be  N.  38  5'  E., 
whereas,  the  direct  course  by  the  compass  from  l  to  b,  (calculated  by  Mercator's 
Sailing)  is  S  50°  6'  W.,  and  from  b  to  l  it  is  N  50°  6'  E.  If  we  assume  any  num- 
ber of  points  on  the  arc  l  b,  the  angle  of  position  between  l  and  each  of  these 
points  will  be  invariable  ;  viz.  p  l  v,  p  l  p  l  t/,  p  l  s,  p  l  r,  &c.  are  each  equal  to 
68°  57' ;  while  the  angle  of  position  between  each  of  these  places  and  l,  viz.  p  w  L, 
p  i  L,  p  y  L,  p  s  L,  p  r  l,  &c.  are  continually  diminishing.  If  a  ship,  therefore,  were 
to  sail  from  l,  on  a  S.  68°  57'  W.  course  by  the  mariner's  compass,  she  would 
never  arrive  at  b  ;  and  were  she  to  sail  from  b,  on  a  N.  38°  5'  E.  course  by  the  com- 
pass, she  would  never  arrive  at  l. 

Hence  an  angle  of  position  between  two  places  cannot  represent  the  bearing,  except 
those  places  be  on  the  equator,  or  upon  the  same  meridian. 


25 


194 


PROBLEMS  PERFORMED  BY 


Part  IIL 


PROBLEM  XVI. 

To  find  the  Antoeci,  Periceci,  and  Antipodes  to  the  inhabitants  of 

any  place. 

Rule.  Place  the  two  poles  of  the  globe  in  the  hoHzon,  and 
bring  the  given  place  to  the  eastern  part  of  the  horizon  ;  then,  if 
the  given  place  be  in  north  latitude,  observe  how  many  degrees 
it  is  to  the  northward  of  the  east  point  of  the  horizon  ;  the  same 
number  of  degrees  to  the  southward  of  the  east  point  will  show 
the  Antoeci ;  an  equal  nnmber  of  degrees,  counted  from  the  west 
point  of  the  horizon  towards  the  north,  will  show  the  Periceci ; 
and  the  same  number  of  degrees,  counted  towards  the  south  of 
the  west,  will  point  out  the  Antipodes.  If  the  place  be  in  south 
latitude,  the  same  rule  will  serve  by  reading  south  for  north  and 
the  contrary. 

OR  THUS  : 

For  the  Antoeci,  Bring  the  given  place  to  the  brass  meridian 
and  observe  its  latitude,  then  in  the  opposite  hemisphere,  under 
the  same  degree  of  latitude,  you  will  find  the  Antoeci. 

For  the  Perioeci.  Bring  the  given  place  to  the  brass  meridian, 
and  set  the  index  of  the  hour  circle  to  12,  turn  the  globe  half 
round,  or  till  the  index  points  to  the  other  12,  then  under  the  lat- 
itude of  the  given  place  you  wnll  find  the  Perioeci. 

For  the  Antipodes.  Bring  the  given  place  to  the  brass  merid- 
ian, and  set  the  index  of  the  hour  circle  to  12,  turn  the  globe  half 
round,  or  till  the  index  points  to  the  other  12,  then  under  the  same 
degree  of  latitude  with  the  given  place,  but  in  the  opposite  hem- 
isphere, you  will  find  the  Antipodes. 

Examples.  1.  Required  the  Antoeci,  Perioeci,  and  Antipodes 
to  the  inhabitants  of  the  island  of  Bermudas. 

Jlnsioer.  Their  AntcBci  are  situated  in  Paraguay,  a  little  N.  W.  of  Buenos  Ayres ; 
their  Peria3ci  in  China,  N.  W.  of  Nankin  j  and  their  Antipodes  in  the  S.  W.  part 
of  New  Holland. 

2.  Required  the  Antceci,  Perioeci,  and  Antipodes  to  the  inhab- 
itants of  the  Cape  of  Good  Hope. 

3.  Captain  Cook,  in  one  of  his  voyages,  was  in  50  degrees 
south  latitude  and  180  degrees  of  longitude  ;  in  what  part  of 
Europe  were  his  Antipodes  ? 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


195 


4.  Required  the  iVntoici  to  the  inhabitants  of  the  Falkland 
islands. 

5.  Required  the  Perioeci  to  the  inhabitants  of  the  Phillipine 
islands. 

6.  What  inhabitants  of  the  earth  are  Antipodes  to  those  of 
Buenos  Ay  res  ? 

PROBLEM  XYII. 

To  find  at  what  rate  per  hour  the  inhabitants  of  any  given  place 
are  carried^  from  west  to  cast,  by  the  revolution  of  the  earth 
on  its  axis. 

Rule.  Find  how  many  miles  make  a  degree  of  longitude  in 
the  latitude  of  the  given  place  (by  Problem  XIII.)  which  multiply 
by  15  for  the  answer.* 

Or,  look  for  the  latitude  of  the  given  place  in  the  table,  Prob- 
lem IX.,  against  which  you  will  find  the  number  of  miles  contain- 
ed in  one  degree  ;  multiply  these  miles  by  15,  and  reject  two  fig- 
ures from  the  right  hand  of  the  product ;  the  result  will  be  the 
answer. 

Examples.  1.  At  what  rate  per  hour  are  the  inhabitants  of 
Madrid  carried  from  west  to  east  by  the  revolution  of  the  earth 
on  its  axis  ? 

-  Answer*  The  latitude  of  Madrid  is  about  40'>  N.  where  a  degree  of  longitude 
measures  46  geographical,  or  nearly  53  English  miles  (see  Example  1.  Prob.  XIII.) 
Now  46  multiplied  by  15  produces  690;  and  53  multipled  by  15  produces  795  ; 
hence  the  inhabitants  of  Madrid  are  carried  690  geographical,  or  795  English  miles 

per  hour. 

By  the  Table. — Against  the  latitude  40  you  will  find  45*96  geographical  miles, 
and  52-87  English  miles ;  hence,  45-96  X  15=689-40  and  52-87  X  15=793-05,  and 
thus  the  required  results  are  689  geographical  or  793  Enghsh  miles. 

Note.  The  answers  found  by  this  rule  should  be  augmented  by  the  360th  part 
to  have  the  solution  accurate,  because  the  earth  by  its  rotation  on  its  axis  describes 
one  complete  revolution  and  nearly  one  degree  besides,  in  the  space  of  a  mean  solar 
day :  hence  the  preceding  results  should  be  increased  by  two  miles  nearly,  and  thus 
the  correct  answer  691  geographical  or  795  English  miles. 

1.  At  what  rate  per  hour  are  the  inhabitants  of  the  following 
places  carried  from  west  to  east  by  the  revolution  of  the  earth  on 
its  axis  ? 

Skalholt 

Spitzbergen 

Petersburg 

London 

*  The  reason  of  this  rule  is  obvious,  for  if  m  be  the  number  of  miles  contained 
in  a  degree,  we  have  24  hours  :  360°  X  n^-  •  1  hour  :  the  answer ;  but,  24  is  con- 
tained 15  times  in  360  ;  therefore  1  hour  :  15  X  1  hour  :  the  answer;  that  is, 
on  a  supposition  that  the  earth  turns  on  its  axis  from  west  to  east  in  24  hours ;  but 
we  have  before  observed  that  it  turns  on  its  axis  in  23  hours  56  min,  4  sec,  which 
will  make  a  small  difference  not  worth  notice. 


Philadelphia  Cape  of  Good  Hope 

Cairo  Calcutta 

Barbadoes  Delhi 

Quito  Batavia. 


PROBLEMS  PERFORMED  BY  Part  III. 


PROBLEM  XVIII. 

A  particular  place,  and  the  hour  of  the  day  at  that  place  being 
given  to  find  what  hour  it  is  at  any  other  place. 

Rule.  Bring  the  place  at  which  the  time  is  given  to  the  brass 
meridian,  and  set  the  index  of  the  hour  circle  to  12  turn  the 
globe  till  the  other  place  comes  to  the  meridian,  and  the  hours 
passed  over  by  the  index  will  be  the  difference  of  time  between 
the  two  places.  If  the  place  where  the  hour  is  sought  lie  to  the 
east  of  that  wherein  the  time  is  given,  count  the  difference  of 
time  forward  from  the  given  hour ;  if  it  lie  to  the  west,  reckon 
the  difference  of  time  backward. 

Or,  without  the  hour  circle. 

Find  the  difference  of  longitude  between  the  two  places  (by 
Problem  VIII.)  and  turn  it  into  lime  by  allowing  15  degrees  to  an 
hour,  or  four  minutes  of  time  to  one  degree.  The  difference  of 
longitude  in  time  will  be  the  difference  of  time  between  the  two 
places,  with  which  proceed  as  above.  Degrees  of  longitude  may 
be  turned  into  time  by  multiplying  by  4 ;  observing  that  minutes 
or  miles  of  longitude,  when  multiplied  by  4,  produce  seconds  of 
time,  and  degrees  of  longitude,  when  multiplied  by  4,  produce 
minutes  of  time. 

It  has  been  remarked  in  the  note,  page  29,  that  some  globes  have  two  rows  of 
figures  on  the  hour  circle,  others  but  one :  this  difference  frequently  occasions  con- 
fusion ;  and  the  manner  in  which  authors  in  general  direct  a  learner  to  solve  those 
problems  wherein  the  hour  circle  is  used,  serves  only  to  increase  that  confusion. 
In  this,  and  in  all  the  succeeding  problems,  great  care  has  been  taken  to  render  the 
rules  general  for  any  hour  circle  whatsoever. 

Examples.  1.  When  it  is  ten  o'clock  in  the  morning  at  Lon- 
don, what  hour  is  it  at  Petersburg  ? 

Answer.  The  difference  of  time  is  two  hours ;  and,  as  Petersburg  is  eastward  of 
London,  this  difference  must  be  counted  forward,  so  that  it  is  12  o'ciock  at  noon  at 
Petersburg. 

Or,  The  difference  of  longitude  between  Petersburg  and  London  is  30°  25', 
which  multiplied  by  4  produces  two  hours  1  min.  40  sec.  the  difference  of  time 
shown  by  the  clocks  of  London  and  Petersburg:  hence  as  Petersburg  lies  to  the 
east  of  London,  when  it  is  ten  o'clock  in  the  morning  at  London,  it  is  one  minute 
and  forty  seconds  past  twelve  at  Petersburg. 


*  The  index  may  be  set  to  any  hour,  but  12  is  the  most  convenient  to  count 
fiom,  and  it  is  immaterial  from  which  12  on  the  hour  circle  the  index  is  set  to. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


197 


2.  When  it  is  two  o'clock  in  the  afternoon  at  Alexandria  in 
Egypt,  what  hour  is  it  at  Philadelphia  ? 

Jlnsxoer.  The  difference  of  time  is  7  hours ;  and  because  Philadelphia  lies  to  the 
westward  of  Alexandria,  this  difference  must  be  reckoned  backward,  so  that  it  is 
7  o'clock  in  the  morning  at  Philadelphia. 

Or,       The  longitude  of  Alexandria  is  30°  16' E. 

The  longitude  of  Philadelphia  is  75   19  W. 

Difference  of  longitude  105  35 

4 

Difference  of  longitude  in  time  7  h.  2  m.  20  sec, 
the  clocks  at  Philadelphia  are  slower  than  those  of  Alexandria;  hence  when  it  is 
two  o'clock  in  the  afternoon  at  Alexandria,  it  is  57  m.  40  sec.  past  six  in  the  morn- 
ing at  Philadelphia. 

3.  When  it  is  noon  at  London,  what  hour  is  it  at  Calcutta  ? 

4.  When  it  is  ten  o'clock  in  the  morning  at  London,  what  hour 
is  it  at  Washington  ? 

5.  When  it  is  nine  o'clock  in  the  morning  at  London,  what 
o'clock  is  it  at  Madras  ? 

6.  My  watch  was  well  regulated  at  London,  and  when  I  arrived 
at  Madras,  which  was  after  a  five  months'  voyage,  it  was  four 
hours  and  fifty  minutes  slower  than  the  clocks  there.  Had  it 
gained  or  lost  during  the  voyage  ?  and  how  much  ? 

PROBLEM  XIX. 

A  particular  place  and  the  hour  of  the  day  being  given,  to  find  all 
places  on  the  globe  where  it  is  then  noon,  or  any  other  given 
hour. 

Rule.  Bring  the  given  place  to  the  brass  meridian,  and  set  the 
index  of  the  hour  circle  to  12 ;  then,  as  the  difference  of  time  be- 
tween the  given  and  required  places,  is  always  known  by  the 
problem,  if  the  hour  at  the  required  places  be  earlier  than  the 
hour  at  the  given  place,  turn  the  globe  eastward  till  the  index  has 
passed  over  as  many  hours  as  are  equal  to  the  given  difference 
of  time ;  but,  if  the  hour  at  the  required  places  be  later  than  the 
hour  at  the  given  place,  turn  the  globe  westward  till  the  index  has 
passed  over  as  many  hours  as  are  equal  to  the  given  difference  of 
time ;  and,  in  each  case,  all  the  places  required  will  be  found 
under  the  brass  meridian. 

Or,  without  the  hour  circle. 

Reduce  the  difference  of  time  between  the  given  place  and  the 
required  places  into  minutes ;  these  minutes,  divided  by  4,  will 


198 


PROBLEMS  PERFORMED  BY 


Part  III. 


give  degrees  of  longitude  ;  if  there  be  a  remainder  after  dividing 
by  4,  naultiply  it  by  60,  and  divide  the  product  by  four,  the  quo- 
tient will  be  minutes  or  miles  of  longitude.  The  difference  of 
longitude  between  the  given  place  and  the  required  places  being 
thus  determined,  if  the  hour  at  the  required  places  be  earlier  than 
the  hour  at  the  given  place,  the  required  places  lie  so  many  de- 
grees to  the  westward  of  the  given  place  as  are  equal  to  the  dif- 
ference of  longitude  ;  if  the  hour  at  the  required  places  be  later 
than  the  hour  at  the  given  place,  the  required  places  lie  so  many 
degrees  to  the  eastward  of  the  given  place  as  are  equal  to  the 
difference  of  longitude. 

Examples.  1.  When  it  is  noon  at  London,  at  what  place  is 
it  half-past  eight  o'clock  in  the  morning  ? 

Answer.  The  difference  of  time  between  London,  the  given  place,  and  the  required' 
places,  is  3^  hours,  and  the  time  at  the  required  places  is  earlier  than  that  at  Lon- 
don ;  therefore  the  required  places  lie  3^  hours  westward  of  London :  consequent- 
ly, by  bringing  London  to  the  brass  meridian,  setting  the  index  to  12,  and  turning 
the  globe  eastward  till  the  index  has  passed  over  3^  hours,  all  the  required  places 
will  be  under  the  brass  meridian,  as  the  eastern  coast  of  Newfoundland,  Cayenne, 
part  of  Paraguay,  &c. 

Or,  The  difference  of  time  between  London,  the  given  place,  and  the  required 
places,  is  3  hours  30  min. 

3  h.  30  m.  The  difference  of  longitude  between  the  given  place 

60  and  the  required  places  is  52°  30'.    The  hour  at  the 

■  required  places  being  earlier  than  that  at  the  given 

4)  120  m.  place,  they  he  52°  30'  westward  of  the  given  place. 

  Hence,  all  places  situated  in  52°  30'  west  longitude 

52= — 2  from  London,  are  the  places  sought,  and  will  be  found 

60  to  be  Cayenne,  &c.  as  above. 

4(120 


30  m. 


2.  When  it  is  two  o'clock  in  the  afternoon  at  London,  at  what 
place  is  it  |  past  five  in  the  afternoon  ? 

Answer.  Here  the  difference  of  time  between  London,  the  given  place,  and  the 
required  places,  is  3^  hours  ;  but  the  time  at  the  required  places  is  later  than  at 
London.  The  operation  will  be  the  same  as  in  example  1,  only  the  globe  must  be 
turned  3^  hours  towards  the  west,  because  the  required  places  will  be  in  east  longi- 
tude, or  eastward  of  the  given  place.  The  places  sought  are  the  Caspian  Sea, 
Western  part  of  NovaZembla,  the  island  ofSocotra,  eastern  part  of  Madagascar,  &c. 

3.  When  it  is  |  past  four  in  the  afternoon  at  Paris,  where  is  it 
noon  ? 

4.  When  it  is  |  past  seven  in  the  morning  at  Ispahan,  where  is 
it  noon  ? 

5.  When  it  is  noon  at  Madras,  where  is  it  i  past  six  o'clock  in 
the  morning  ? 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


199 


6.  At  sea  in  latitude  40°  north,  when  it  was  ten  o'clock  in  the 
morning  by  the  time-piece,  which  shows  the  hour  at  London,  it 
was  exactly  nine  o'clock  in  the  morning  at  the  ship,  by  a  correct 
celestial  observation.    In  what  part  of  the  ocean  was  the  ship  ? 

7.  When  it  is  noon  at  London,  what  inhabitants  of  the  earth 
have  midnight? 

8.  When  it  is  ten  o'clock  in  the  morning  at  London,  where  is 
it  ten  o'clock  in  the  evening  ? 

PROBLEM  XX. 

To  find  the  sun's  longitude  {commonly  called  the  sun's  place  in  the 
ecliptic)  and  his  declination. 

Rule.  Look  for  the  given  day  in  the  circle  of  months  on  the 
horizon,  against  which,  in  the  circle  of  signs,  are  the  sign  and 
degree  in  which  the  sun  is  for  that  day.  Find  the  same  sign 
and  degree  in  the  ecliptic  on  the  surflice  of  the  globe ;  bring  the 
degree  of  the  ecliptic,  thus  found,  to  that  part  of  the  brass  merid- 
ian which  is  numbered  from  the  equator  towards  the  poles,  its 
distance  from  the  equator  reckoned  on  the  brass  meridian,  is  the 
sun's  declination. 

This  problem  may  he  performed  hy  the  celestial  globe,  using  the 
same  rule. 

Or,  by  the  analemma.* 

Bring  the  analemma  to  that  part  of  the  brass  meridian  which  is 
numbered  from  the  equator  towards  the  poles,  and  the  degree  on 
the  brass  meridian,  exactly  above  the  day  of  the  month,  is  the 
sun's  declination.    Turn  the  globe  till  a  point  of  the  ecliptic,  cor- 


*  The  Analemma  is  properly  an  orthrographic  projection  of  the  sphere  on  the 
plane  of  the  meridian  ;  but  what  is  called  the  Analemma  on  the  globe  is  a  narrow 
slip  of  paper,  the  length  of  which  is  equal  to  the  breadth  of  the  torrid  zone.  It  is 
pasted  on  some  vacant  place  on  the  globe  in  the  torrid  zone,  and  is  divided  into 
months,  and  days  of  the  months,  corresponding  to  the  sun's  declination  for  every 
day  in  the  year.  It  is  divided  into  two  parts ;  the  right-hand  part  begins  at  the 
winter  solstice,  or  December  21st,  and  is  reckoned  upwards  towards  the  summer 
solstice,  or  June  21st,  where  the  left-hand  part  begins,  which  is  reckoned  down- 
wards in  a  similar  manner,  or  towards  the  winter  solstice.  On  Cart's  globes  the 
Analemma  somewhat  resembles  the  figure  8.  It  appears  to  have  been  drawn  in 
this  shape  for  the  convenience  of  shewing  the  equation  of  time,  by  means  of  a 
straight  line  which  passes  through  the  middle  of  it.  The  equation  of  time  is  placed 
on  the  horizon  of  Bardin's  globes. 


200 


PROBLEMS  PERFORMED  BY 


Part  III. 


responding  to  the  day  of  the  month,  passes  under  the  degree  of 
the  sun's  declination,  that  point  will  be  the  sun's  longitude  or 
place  for  the  given  day.  If  the  sun's  declination  be  north,  and 
increasing,  the  sun's  longitude  will  be  somewhere  between  Aries 
and  Cancer.  If  the  declination  be  decreasing,  the  longitude  will 
be  between  Cancer  and  Libra.  If  the  sun's  declination  be  south, 
and  increasing,  the  sun's  longitude  will  be  between  Libra  and 
Capricorn ;  if  the  declination  be  decreasing,  the  longitude  will 
be  between  Capricorn  and  Aries. 

The  sun's  longitude  and  declination  are  given  in  the  second  page  of  every  month, 
in  the  J^autical  Almanac,  for  every  day  in  that  month  5  they  are  likewise  given  in 
White's  Ephemeris,  for  every  day  in  the  year. 

Examples.  1.  What  is  the  sun's  longitude  and  declination  on 
the  15th  of  April? 

Answer.    The  sun's  place  is  26°  in  T'j  declination  10'  N. 

2.  Required  the  sun's  place  and  declination  for  the  following 


days. 


January  21. 
February  7. 
March  16. 
April  8. 


May  18. 
June  11. 
July  11. 
August  1. 


September  9. 
October  16. 
November  17. 
December  1. 


PROBLEM  XXI. 

To  place  the  globe  in  the  same  situation  with  respect  to  the 
SUN,  as  our  earth  is  at  the  Equinoxes,  at  the  summer  solstice, 
and  at  the  winter  solstice,  and  thereby  to  show  the  compar- 
ative lengths  of  the  longest  and  shortest  days* 

I.  For  the  Equinoxes.  Place  the  two  poles  of  the  globe  in 
,the  horizon :  for  at  this  time  the  sun  has  no  declination,  being 
in  the  equinoctial  in  the  heavens,  which  is  an  imaginary  line 
standing  vertically  over  the  equator  on  the  earth.  Now,  if  we 
suppose  the  sun  to  be  fixed,  at  a  considerable  distance  from  the 
globe,  vertically  over  that  point  of  the  brass  meridian  which  is 
marked  o,  it  is  evident  that  the  wooden  horizon  will  be  the  bound- 
ary of  light  and  darkness  on  the  globe,  and  that  the  upper  hem- 
isphere will  be  enlightened  from  pole  to  pole. 


*  In  this  problem,  as  in  all  others  vv^here  the  pole  is  elevated  to  the  sun's  declin- 
ation, the  sun  is  supposed  to  be  fixed,  and  the  earth  to  move  on  its  axis  from  west 
to  east.  The  author  of  this  work  has  a  little  brass  ball  made  to  represent  the  sun  ; 
this  ball  is  fixed  upon  a  strong  wire,  and  when  used,  slides  out  of  a  socket  like  an 
acromatic  telescope.  The  socket  is  made  to  screw  to  the  brass  meridian  (of  any 
globe)  over  the  sun's  declination,  and  the  little  brass  ball  representing  the  sun, 
stands  over  the  declination,  at  a  considerable  distance  from  the  globe. 


Chap.  I. 


THE   TERRESTRIAL  GLOBE. 


201 


Meridians,  or  lines  of  longitude,  being  generally  drawn  on  the 
globe  through  every  15  degrees  of  the  equator,  the  sun  will  ap- 
parently pass  from  one  meridian  to  anotlier  in  an  hour.  If  you 
bring  the  point  Aries  on  the  equator  to  the  eastern  part  of  the  ho- 
rizon, the  point  Libra  will  be  in  the  western  part  thereof;  and  the 
sun  will  appear  to  be  setting  to  the  inhabitants  of  London*  and 
to  all  places  under  the  same  meridian :  let  the  globe  be  now 
turned  gently  on  its  axis  towards  the  east,  the  sun  will  appear  to 
move  towards  the  west,  and,  as  the  different  places  successively 
enter  the  dark  hemisphere,  the  sun  will  appear  to  be  setting  in  the 
west.  Continue  the  motion  of  the  globe  eastward,  till  London 
comes  to  the  western  edge  of  the  horizon  ;  the  moment  it  emerges 
above  the  horizon,  the  sun  will  appear  to  be  rising  in  the  east. 
If  the  motion  of  the  globe  on  its  axis  be  continued  eastward,  the 
sun  will  appear  to  rise  higher  and  higher,  and  to  move  towards 
the  west ;  when  London  comes  to  the  brass  meridian,  the  sun 
wmII  appear  at  its  greatest  height ;  and  after  London  has  passed 
the  brass  meridian,  he  will  continue  his  apparent  motion  west- 
ward, and  gradually  diminish  in  altitude  till  London  comes  to  the 
eastern  part  of  the  horizon,  when  he  will  again  be  setting.  Du- 
ring this  revolution  of  the  earth  on  its  axis,  every  place  on  its 
surface  has  been  twelve  hours  in  the  dark  hemisphere,  and  twelve 
hours  in  the  enlightened  hemisphere  ;  consequently  the  days  and 
nights  are  equal  all  over  the  world  ;  for  all  the  parallels  of  lati- 
tude are  divided  into  two  equal  parts  by  the  horizon,  and  in  eve- 
ry degree  of  latitude  there  are  six  meridians  between  the  eastern 
part  of  the  horizon  and  the  brass  meridian ;  each  of  these  me- 
ridians answers  to  one  hour,  hence  half  the  length  of  the  day  is 
six  hours,  and  the  whole  length  twelve  hours. 

If  any  place  be  brought  to  the  brass  meridian,  the  number  of 
degrees  between  that  place  and  the  horizon  (reckoned  the  near- 
est way)  will  be  the  sun's  meridian  altitude.  Thus,  if  London  be 
brought  to  the  meridian,  the  sun  will  then  appear  exactly  south, 
and  its  altitude  will  be  38^^  degrees  ;  the  sun's  meridian  altitude 
at  Philadelphia  will  be  50  degrees  ;  his  meridian  altitude  at  Quito 
90  degrees ;  and  here,  as  in  every  place  on  the  equator,  as  the 
globe  turns  on  its  axis,  the  sun  will  be  vertical.  At  the  Cape  of 
Good  Hope  the  sun  will  appear  due  north  at  noon,  and  his  alti- 
tude will  be  55^  degrees. 


*  Tlie  meridian  of  London  is  licre  supposed  to  pass  through  the  equinoctial 
point  Aries,  on  the  best  modern  globes. 

2G 


202 


PROBLEMS  PERFORMED  BY 


Part  III. 


2.  For  the  summer  solstice. — The  summer  solstice,  to  the 
inhabitants  of  north  latitude,  happens  on  the  21st  of  June,  when 
the  sun  enters  Cancer,  at  which  time  his  declination  is  23°  28' 
north.  Elevate  the  north  pole  23i  degrees  above  the  northern 
point  of  the  horizon,  bring  the  sign  of  Cancer  in  the  ecliptic  to 
the  brass  meridian,  and  over  that  degree  of  the  brass  meridian 
under  which  this  sign  stands,  let  the  sun  be  supposed  to  be  fixed 
at  a  considerable  distance  from  the  globe. 

While  the  globe  remains  in  this  position,  it  will  be  seen  that  the 
equator  is  exactly  divided  into  two  equal  parts,  the  equinoctial 
point  Aries  being  in  the  western  part  of  the  horizon,  and  the  op- 
posite point  Libra  in  the  eastern  part,  and  between  the  horizon 
and  the  brass  meridian  (counting  on  the  equator)  there  are  six 
meridians,  each  15  degrees,  or  an  hour  apart,  consequently  the 
day  at  the  equator  is  12  hours  long.  From  the  equator  north- 
ward as  far  as  the  arctic  circle,  the  diurnal  arcs  will  exceed  the 
nocturnal  arcs;  that  is,  more  than  one  half  of  any  of  the  paral- 
lels of  latitude  will  be  above  the  horizon,  and  of  course  less  than 
one  half  will  be  below,  so  that  the  days  are  longer  than  the  nights. 
All  the  parallels  of  latitude  within  the  Arctic  circle  will  be 
wholly  above  the  horizon,  consequently  those  inhabitants  will 
have  no  night.  From  the  equator  southward,  as  far  as  the  An- 
tarctic circle,  the  nocturnal  arcs  will  exceed  the  diurnal  arcs : 
that  is,  more  than  one  half  of  any  of  the  parallels  of  latitude  will 
be  below  the  horizon,  and  consequently  less  than  one  half  will 
be  above.  All  the  parallels  of  latitude  within  the  Antarctic  cir- 
cle, will  be  wholly  below  the  horizon,  and  the  inhabitants,  if  any^ 
will  have  twilight  or  dark  night. 

From  a  little  attention  to  the  parallels  of  latitude,  while  the 
globe  remains  in  this  position,  it  will  easily  be  seen  that  the  arcs 
of  those  parallels  which  are  above  the  horizon,  north  of  the  equa- 
tor, are  exactly  of  the  same  length  as  those  below  the  horizon, 
south  of  the  equator;  consequently,  when  the  inhabitants  of 
north  latitude  have  the  longest  day,  those  in  south  latitude  have 
the  longest  night.  It  will  likewise  appear,  that  the  arcs  of  those 
parallels  which  are  above  the  horizon,  south  of  the  equator,  are 
exactly  of  the  same  length  as  those  below  the  horizon  north  of 
the  equator;  therefore,  when  the  inhabitants  who  are  situated 
south  of  the  equator  have  the  shortest  day,  those  who  live  north 
of  the  equator  have  the  shortest  night. 

By  counting  the  number  of  meridians,  (supposing  them  to  be 
drawn  through  every  fifteen  degrees  of  the  equator,)  between  the 
horizon  and  the  brass  meridian,  on  any  parallel  of  latitude,  half 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


203 


the  length  of  the  day  will  be  determined  in  that  latitude,  the 
double  of  which  is  the  length  of  the  day. 

1.  In  the  parallel  of  20  degrees  north  latitude,  there  are  six 
meridians  and  two  thirds  more,  hence  the  longest  day  is  13  hours 
and  20  minutes  ;  and,  in  the  parallel  of  20  degrees  south  latitude, 
there  are  five  meridians  and  one  third,  hence  the  shortest  day  ia 
that  latitude  is  10  hours  and  40  minutes. 

2.  In  the  parallel  of  30  degrees  north  latitude,  there  are  seven 
meridians  between  the  horizon  and  the  brass  meridian,  hence  the 
longest  day  is  14  hours  ;  and  in  the  same  degree  of  south  latitude 
there  are  only  five  meridians,  hence  the  shortest  day  in  that 
latitude  is  ten  hours. 

3.  In  the  parallel  of  50  degrees  north  latitude  there  are  eight 
meridians  between  the  horizon  and  the  brass  meridian  ;  the 
longest  day  is  therefore  sixteen  hours  ;  and  in  the  same  degree  of 
south  latitude,  there  are  only  four  meridians  ;  hence  the  shortest 
day  is  eight  hours. 

4.  In  the  parallel  of  60  degrees  north  latitude,  there  are  9J 
meridians  from  the  horizon  to  the  brass  meredian,  hence  the 
longest  day  is  I8|  hours  ;  and  in  the  same  degree  of  south  latitude, 
there  are  only  2|  meridians,  the  length  of  the  shortest  day  is 
therefore  hours. 

By  turning  the  globe  gently  round  on  its  axis  from  west  to  east, 
we  shall  readily  perceive  that  the  sun  will  be  vertical  to  all  the 
inhabitants  under  the  tropic  of  Cancer,  as  the  places  successively 
pass  the  brass  meridian. 

If  any  place  be  brought  to  the  brass  meridian,  the  number  of 
degrees  between  that  place  and  the  horizon  (reckoned  the  nearest 
way)  will  show  the  sun's  meridian  altitude.  Thus,  at  London, 
the  sun's  meridian  altitude  will  be  found  to  be  about  62  degrees ; 
at  Petersburgh  54J  degrees,  at  Madrid  73  degrees,  &;c.  To  the 
inhabitants  of  these  places  the  sun  appears  due  south  at  noon.  At 
Madras  the  sun's  meridian  altitude  will  be  79i  degrees,  at  the 
Cape  of  Good  Hope  32  degrees,  at  Cape  Horn  10|  degrees,  &c. 
The  sun  will  appear  due  north  to  the  inhabitants  of  these  places 
at  noon.  If  the  southern  extremity  of  Spitzbergen,  in  latitude 
76|  north,  be  brought  to  that  part  of  the  brass  meridian  which 
is  numbered  from  the  equator  towards  the  poles,  the  sun's 
meridian  altitude  will  be  37  degrees,  which  is  its  greatest  altitude ; 
and  if  the  globe  be  turned  eastward  twelve  hours  or  till 
Spitzbergen  comes  to  that  part  of  the  brass  meridian  which  is 
numbered  from  the  pole  towards  the  equator,  the  sun's  altitude 
will  be  ten  degrees,  which  is  its  least  altitude  for  the  day  given  in 
the  problem.    It  was  shown,  in  the  foregoing  part  of  the  problem, 


204 


PROBLEMS  PERFORMED  BY 


Part  III. 


that,  when  the  sun  is  vertically  over  the  equator  in  the  vernal 
equinox,  the  north  pole  begins  to  be  enlightened,  consequently 
the  farther  the  sun  apparently  proceeds  in  its  course  northward, 
the  more  day-light  will  be  diffused  over  the  north  polar  regions, 
and  the  sun  will  appear  gradually  to  increase  in  altitude  at  the 
north  pole,  till  the  21st  of  June,  when  his  greatest  height  is  23  J 
degrees ;  he  will  then  gradually  diminish  in  height  till  the  23d  of 
September,  the  time  uf  the  autumnal  equinox,  when  he  will  leave 
the  north  pole,  and  proceed  towards  the  south  ;  consequently 
the  sun  has  been  visible  at  the  north  pole  for  six  months. 

3.  For  the  Winter  Solstice. — The  winter  solstice,  to  the 
inhabitants  of  north  latitude,  happens  on  the  21st  of  December, 
when  the  sun  enters  Capricorn,  at  which  time  his  declination  is 
23  28  south.  Elevate  the  south  pole  23|  degrees  above  the 
southern  point  of  the  horizon,  bring  the  sign  of  Capricorn  in  the 
ecliptic  to  the  brass  meridian,  and  over  that  degree  of  the  brass 
meridian  under  which  this  sign  stands  let  the  sun  be  supposed  to 
be  fixed  at  a  considerable  distance  from  the  globe. 

Here,  as  at  the  summer  solstice,  the  days  at  the  equator  will  be 
twelve  hours  long,  but  the  equinoctial  point  Aries  will  be  in  the 
eastern  part  of  the  horizon,  and  Libra  in  the  western.  From  the 
equator  southward,  as  far  as  the  Antarctic  circle,  the  diurnal  arcs 
will  exceed  the  nocturnal  arcs.  All  the  parallels  of  latitude 
within  the  Antarctic  circle  will  be  wholly  above  the  horizon. 
From  the  equator  northward,  the  nocturnal  arcs  will  exceed  the 
diurnal  arcs.  All  the  parallels  of  latitude  within  the  Arctic  circle 
will  be  equally  below  the  horizon.  The  inhabitants  south  of  the 
equator  will  now  have  their  longest  day,  while  those  on  the  north 
of  the  equator  will  have  their  shortest  day. 

As  the  g!obe  turns  on  its  axis  from  west  to  east,  the  sun  will 
be  vertical  successively  to  all  the  inhabitants  under  the  tropic  of 
Capricorn.  By  bringing  any  place  to  the  brass  meridian,  and 
finding  the  sun's  meridian  altitude  (as  in  the  foregoing  part  of  the 
problem),  the  greatest  altitudes  will  be  in  south  latitude,  and  the 
least  in  the  north  ;  contrary  to  what  they  were  before.  Thus,  at 
London,  the  sun's  greatest  altitude  will  be  only  15  degrees,  instead 
of  62  ;  and  its  greatest  altitude  at  Cape  Horn  will  now  be  57J 
degrees,  instead  of  IQi,  as  at  the  summer  solstice ;  hence  it  appears 
that  the  difference  between  the  sun's  greatest  and  least  meridian 
altitude  at  any  place  in  the  temperate  zone,  is  equal  to  the  breadth 
of  the  torrid  zone,  viz.  47  degrees,  or  more  correctly  46''  56'. 
On  the  23d  of  September,  when  the  sun  enters  Libra,  that  is,  at 
the  time  of  the  autumnal  equinox,  the  south  pole  begins  to  be 
enlightened,  and,  as  the  sun's  declination  increases  southward,  he 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


205 


will  shine  farther  over  the  south  pole,  and  gradually  increase  in 
altitude  at  the  pole ;  for,  at  all  times,  his  altitude  at  either  pole  is 
equal  to  his  declination.  On  the  21st  of  December,  the  sun  will 
have  the  greatest  south  declination,  after  which  his  aUitude  at  the 
south  pole  will  gradually  diminish  as  his  declination  diminishes ; 
and  on  the  21st  of  March,  when  the  sun's  declination  is  nothing, 
he  will  appear  to  skim  along  the  horizon  at  the  south  pole,  and 
likewise  at  the  north  pole  ;  the  sun  has  therefore  been  visible  at 
the  south  pole  for  six  months. 


PROBLEM  XXII. 

To  place  the  globe  in  the  same  situation,  with  respect  to  the 
Polar  Star  in  the  heavens,  as  our  earth  is  to  the  inhabitants  of 
the  equator,  SfC.  viz.  to  illustrate  the  three  positions  of  the  sphere, 
right,  parallel  and  oblique,  so  as  to  show  the  comparative 
length  of  the  longest  and  shortest  days.* 

1.  For  the  Right  Sphere.  The  inhabitants  who  live  upon 
the  equator  have  a  right  sphere,  and  the  north  polar  star  appears 
always  in  (or  very  near)  the  horizon.  Place  the  two  poles  of  the 
globe  in  the  horizon,  then  the  north  pole  will  correspond  with  the 
north  polar  star,  and  all  the  heavenly  bodies  will  appear  to  revolve 
round  the  earth  from  east  to  west,  in  circles  parallel  to  the  equi- 
noctial, according  to  their  different  declinations :  one  half  of  the 
starry  heavens  will  be  constantly  above  the  horizon,  and  the  other 
half  below,  so  that  the  stars  will  be  visible  for  twelve  hours,  and 
invisible  for  the  same  space  of  time  ;  and,  in  the  course  of  a  year, 
an  inhabitant  upon  the  equator  may  see  all  the  stars  in  the 
heavens.  The  ecliptic  being  drawn  on  the  terrestrial  globe,  young 
students  are  often  led  to  imagine  that  the  sun  apparently  moves 
daily  round  the  earth  in  the  same  oblique  manner.  To  correct 
this  false  idea,  we  must  suppose  the  ecliptic  to  be  transferred  to 
the  heavens,  where  it  properly  points  out  the  sun's  apparent  an- 
nual path  amongst  the  fixed  stars.  The  sun's  diurnal  path 
is  either  over  the  equator,  as  at  the  time  of  the  equinoxes,  or  in 


*  In  this  problem,  and  in  all  others  where  the  pole  is  elevated  to  the  latitude  of 
a  given  place,  the  earth  is  supposed  to  be  fixed,  and  the  sun  to  move  round  it  from 
east  to  west.  When  the  given  place  is  brought  to  the  brass  meridian,  the  wooden 
horizon  is  the  true  rational  horizon  of  that  place,  but  it  does  not  separate  the  en- 
lightened part  of  the  globe  from  the  dark  part,  as  in  the  preceding  problem. 


206 


PROBLEMS  PERFORMED  BY 


Part  III. 


lines  nearly  parallel  to  the  equator ;  this  may  be  correctly  illus- 
trated by  fastening  one  end  of  a  piece  of  packthread  upon  the 
point  Aries  on  the  equator,  and  winding  the  packthread  round  the 
globe  towards  the  right  hand,  so  that  one  fold  may  touch  another, 
till  you  come  to  the  tropic  of  Cancer ;  thus  you  will  have  a  correct 
view  of  the  sun's  apparent  diurnal  path  from  the  vernal  equinox 
to  the  summer  solstice ;  for,  after  a  diurnal  revolution,  the  sun 
does  not  come  to  the  same  point  of  the  parallel  whence  it  departed, 
but,  according  as  it  approaches  to  or  recedes  from  the  tropic, 
is  a  little  above  or  below  that  point.  When  the  sun  is  in  the 
equinoctial,  he  will  be  vertical  to  all  the  inhabitants  upon  the 
equator,  and  his  apparent  diurnal  path  will  be  over  that  line : 
when  the  sun  has  ten  degrees  of  north  declination,  his  apparent 
diurnal  path  will  be  from  east  to  west  nearly  along  that  parallel. 
When  the  sun  has  arrived  at  the  tropic  of  Cancer,  his  diurnal 
path  in  the  heavens  will  be  along  that  line,  and  he  will  be  vertical 
to  all  the  inhabitants  on  the  earth  in  latitude  23^  28'  north.  The 
inhabitants  upon  the  equator  will  always  have  twelve  hours  day 
and  twelve  hours  night,  notwithstanding  the  variation  of  the  sun's 
declination  from  north  to  south,  or  from  south  to  north ;  because 
the  parallel  of  latitude  which  the  sun  apparently  describes  for  any 
day  will  always  be  cut  into  two  equal  parts  by  the  horizon.  The 
greatest  meridian  altitude  of  the  sun  w^ill  be  90  degrees,  and  the 
least  66°  32'.  During  one  half  of  the  year,  an  inhabitant  on  the 
equator  will  see  the  sun  full  north  at  noon,  and  during  the  other 
half  it  w^ill  be  full  south. 

2.  For  the  Parallel  Sphere. — The  inhabitants  (if  any)  who 
live  at  the  north  pole  have  a  parallel  sphere,  and  the  north  polar 
star  in  the  heavens  appears  nearly  over  their  heads.  Elevate  the 
north  pole  ninety  degrees  above  the  horizon,  then  the  equator 
will  coincide  with  the  horizon,  and  all  the  parallels  of  latitude 
will  be  parallel  thereto.  In  the  summer  half-year,  that  is,  from 
the  vernal  to  the  autumnal  equinox,  the  sun  will  appear  above 
the  horizon,  consequently  the  stars  and  planets  will  be  invisible 
during  that  period.  When  the  sun  enters  Aries,  on  the  21st  of 
March,  he  will  be  seen  by  the  inhabitants  of  the  north  pole  (if 
there  be  any  inhabitants)  to  skim  just  along  the  edge  of  the  hori- 
zon :  and  as  he  increases  in  declination,  he  will  increase  in  alti- 
tude, forming  a  kind  of  spiral,  as  before  described,  by  wrapping 
a  thread  round  the  globe.  The  sun's  altitude  at  any  particular 
hour  is  always  equal  to  his  declination.  The  greatest  altitude  the 
sun  can  have  is  23°  28',  at  which  time  he  has  arrived  at  the  tropic 
of  Cancer ;  after  which  he  will  gradually  decrease  in  altitude  as 
his  declination  decreases.    When  the  sun  arrives  at  the  sign 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


207 


Libra,  he  will  again  appear  to  skim  along  the  edge  of  the  horizon, 
after  which  he  will  totally  disappear,  having  been  above  the  ho- 
rizon for  six  months.  Though  the  inhabitants  at  the  north  pole 
will  lose  sight  of  the  sun  a  short  time  after  the  autumnal  equinox, 
vet  the  twilight  will  continue  for  nearly  two  months ;  for  the 
sun  will  not  be  18°  below  the  horizon  till  he  enters  the  20th  of 
Scorpio,  as  may  be  seen  by  the  globe. 

After  the  sun  has  descended  18°  below  the  horizon,  all  the  stars 
in  the  northern  hemisphere  will  become  visible,  and  appear  to 
have  a  diurnal  revolution  round  the  earth  from  east  to  west,  as 
the  sun  appeared  to  have  when  he  was  above  the  horizon.  These 
stars  will  not  set  during  the  winter  half  of  the  year ;  and  the 
planets,  when  they  are  in  any  of  the  northern  signs,  will  be  visi- 
ble. The  inhabitants  under  the  north  polar  star  have  the  moon 
constantly  above  their  horizon  during  fourteen  revolutions  of  the 
earth  on  its  axis,  and  at  every  full  moon  which  happens,  from  the 
23d  of  September  to  the  21st  of  March,  the  moon  is  in  some  of 
the  northern  signs,  and  consequently  visible  at  the  north  pole  ; 
for  the  sun  being  below  the  horizon  at  that  time,  the  moon  must 
be  above  the  horizon,  because  she  is  always  in  that  sign  which  is 
diametrically  opposite  to  the  sun  at  the  time  of  full  moon. 

When  the  sun  is  at  his  greatest  depression  below  the  horizon, 
being  then  in  Capricorn,  the  moon  is  at  her  First  Quarter  in 
Aries :  Full  in  Cancer ;  and  at  her  Third  Quarter  in  Libra : 
and  as  the  beginning  of  Aries  is  the  rising  point  of  the  ecliptic, 
Cancer  the  highest,  and  Libra  the  setting  point,  the  moon  rises  at 
her  First  Quarter  in  Aries,  is  most  elevated  above  the  horizon, 
and  Full  in  Cancer,  and  sets  at  the  beginning  of  Libra  in  her 
Third  Quarter;  having  been  visible  for  fourteen  revolutions  of 
the  earth  on  its  axis,  viz.  during  the  moon's  passage  from  Aries  to 
Libra.  Thus  the  north  pole  is  supplied  one  half  the  winter  time 
with  constant  moonlight  in  the  sun's  absence ;  and  the  inhabit- 
ants only  lose  sight  of  the  moon  from  her  Third  to  her  First 
Quarter,  while  she  gives  but  little  light,  and  can  be  of  little  or 
no  service  to  them. 

3.  For  the  Oblique  Sphere. — Whenever  the  terrestrial 
globe  is  placed  in  a  proper  situation  with  respect  to  the  fixed 
stars,  the  pole  must  be  elevated  as  many  degrees  above  the  hori- 
zon as  are  equal  to  the  latitude  of  the  given  place,  and  the  north 
pole  of  the  globe  must  point  to  the  north  polar  star  in  the  heavens ; 
for  in  sailing,  or  travelling  from  the  equator  northward,  the  north 
polar  star  appears  to  rise  higher  and  higher.  On  the  equator  it 
will  appear  in  the  horizon  ;  in  ten  degrees  of  north  latitude  it  will 
be  ten  degrees  above  the  horizon  ;  in  20"  of  north  latitude  it 


208 


PROBLEMS  PERFORMED  BY 


Part  III, 


will  be  20  degrees  above  the  horizon  :  and  so  on,  always  increas- 
ing in  altitude  as  the  latitude  increases.  Every  inhabitant  of  the 
earth,  except  those  who  live  upon  the  equator,  or  exactly  under 
the  north  polar  star,  has  an  oblique  sphere,  viz.  the  equator  cuts 
the  horizon  obliquely.  By  elevating  and  depressing  the  poles,  in 
several  problems,  a  young  student  is  sometimes  led  to  imagine 
that  the  earth's  axis  moves  northward  and  southward  just  as  the 
pole  is  raised  or  depressed  ;  this  is  a  mistake,  the  earth's  axis  has 
no  such  motion.*  In  travelling  from  the  equator  northward,  our 
horizon  varies ;  thus,  when  we  are  on  the  equator,  the  northern 
point  of  our  horizon  is  exactly  opposite  the  north  polar  star ; 
when  we  have  travelled  to  ten  degrees  north  latitude,  the  north 
point  of  our  horizon  is  ten  degrees  below  the  pole,  and  so  on : 
now,  the  wooden  horizon  on  the  terrestrial  globe  is  immovable, 
otherwise  it  ought  to  be  elevated  or  depressed,  and  not  the  pole  ; 
but  whether  >ve  elevate  the  pole  ten  degrees  above  the  horizon, 
or  depress  the  north  point  of  the  horizon  ten  degrees  below  the 
pole,  the  appearance  will  be  exactly  the  same. 

The  latitude  of  London  is  about  51J  degrees  north  :  if  London 
be  brought  to  the  brass  meridian,  and  the  north  pole  be  elevated 
511  degrees  above  the  north  point  of  the  wooden  horizon,  then 
the  wooden  horizon  will  be  the  true  horizon  of  London  ;  and,  if 
the  artificial  globe  be  placed  exactly  north  and  south  by  a  mari- 
ner's compass,  or  by  a  meridian  line,  it  will  have  exactly  the  posi- 
tion which  the  real  globe  has.  Now,  if  we  imagine  lines  to  be 
drawn  through  every  degreef  within  the  torrid  zone,  parallel  to 
the  equator,  they  will  nearly  represent  the  sun's  diurnal  path  on^ 
any  given  day.  By  comparing  these  diurnal  paths  with  each 
other,  they  will  be  found  to  increase  in  length  from  the  equator 
northward,  and  to  decrease  in  length  from  the  equator  south- 
ward ;  consequently,  when  the  sun  is  north  of  the  equator,  the 
days  are  increasing  in  length  ;  and  when  south  of  the  equator,  the 
days  are  decreasing.  The  sun's  meridian  altitude  for  any  day 
may  be  found  by  counting  the  number  of  degrees  from  the  parallel 
in  which  the  sun  is  on  that  day,  towards  the  horizon,  upon  the  brass 
meridian  ;  thus,  when  the  sun  is  in  that  parallel  of  latitude  which 
is  ten  degrees  north  of  the  equator,  his  meridian  altitude  will  be 
48|  degrees.  Though  the  wooden  horizon  be  the  true  horizon  of 
the  given  place,  yet  it  does  not  separate  the  enlightened  hemis- 
phere of  the  globe  from  the  dark  hemisphere,  when  the  pole  is 
thus  elevated.    For  instance,  when  the  sun  is  in  Aries,  and  Lon- 


*  Tlie  earth's  axis  has  a  kind  of  hbrating  motion,  called  the  nutation,  but  this 
cannot  be  represented  by  elevating  or  depressing  the  pole, 
t  Such  hnes  are  drawn  on  Adams's  globes. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


209 


don  at  the  meridian,  all  the  places  on  the  globe  above  the  hori- 
zon beyond  those  meridians  which  pass  through  the  east  and  west 
points  thereof,  reckoning  towards  the  north,  are  in  darkness,  not- 
withstanding they  are  above  the  horizon :  and  all  places  below 
the  horizon,  have  day-light,  notwithstanding  they  are  below  the 
horizon  of  London. 

PROBLEM  XXIII. 

The  month  and  day  of  the  month  being  given,  to  find  all  places 
of  the  earth  where  the  sun  is  vertical  on  that  day;  those  places 
where  the  sun  does  not  set,  and  those  places  where  he  does  not 
rise  on  the  given  day. 

Rule.  Find  the  sun's  declination  (by  Problem  XX.)  for  the 
given  day,  and  mark  it  on  the  brass  meridian  ;  turn  the  globe 
round  on  its  axis  from  west  to  east,  and  all  the  places  which  pass 
under  this  mark  will  have  the  sun  vertical  on  that  day. 

Secondly,  Elevate  the  north  or  south  pole,  according  as  the 
sun's  declination  is  north  or  south,  so  many  degrees  above  the 
horizon  as  are  equal  to  the  sun's  declination :  turn  the  globe  on 
its  axis  from  west  to  east ;  then,  to  those  places  which  do  not 
descend  below  the  horizon,  in  that  frigid  zone  near  the  elevated 
pole,  the  sun  does  not  set  on  the  given  day :  and  to  those  places 
which  do  not  ascend  above  the  horizon,  in  that  frigid  zone  ad- 
joining to  the  depressed  pole,  the  sun  does  not  rise  on  the  given 
day. 

Or,  by  the  analemma. 

Bring  the  analemma  to  that  part  of  the  brass  meridian  which 
is  numbered  from  the  equator  towards  the  poles,  the  degree  di- 
rectly above  the  day  of  the  month,  on  the  brass  meridian,  is  the 
sun's  declination.  Elevate  the  north  or  south  pole,  according  as 
the  sun's  declination  is  north  or  south,  so  many  degrees  above  the 
horizon  as  are  equal  to  the  sun's  declination ;  turn  the  globe  on 
its  axis  from  west  to  east,  then  to  those  places  which  pass  under 
the  sun's  declination,  on  the  brass  meridian,  the  sun  will  be  ver- 
tical ;  to  those  places  (m  that  frigid  zone  near  the  elevated  pole) 
which  do  not  go  below  the  horizon,  the  sun  does  not  set :  and  to 
those  places  (in  that  frigid  zone  near  the  depressed  pole)  which 
do  not  come  above  the  horizon,  the  sun  does  not  rise  on  the 
given  day. 

27 


210 


PROBLEMS  PERFORMED  BY 


Part  III. 


Examples,  1.  Find  all  places  of  the  earth  where  the  sun  is 
vertical  on  the  llth  of  May,  those  places  in  the  north  frigid  zone 
where  the  sun  does  not  set,  and  those  places  in  the  south  frigid 
zone  where  he  does  not  rise. 

Answer,  The  sun  is  vertical  at  St.  Anthony,  one  of  the  Cape  Verd  islands,  the 
Virgin  islands,  south  of  St.  Domingo,  Jamaica,  Golconda,  &c.  All  the  places 
within  eighteen  degrees  of  the  north  pole  will  have  constant  day ;  and  those  (if 
any)  within  eighteen  degrees  of  the  south  pole  will  have  constant  night. 

2.  Whether  does  the  sun  shine  over  the  north  or  south  pole  on 
the  27th  of  October,  to  what  places  will  he  be  vertical  at  noon, 
what  inhabitants  of  the  earth  will  have  the  sun  below  their  hori- 
zon during  several  revolutions,  and  to  what  part  of  the  globe  will 
the  sun  never  set  on  that  day? 

3.  Find  all  the  places  of  the  earth  where  the  inhabitants  have 
no  shadow  when  the  sun  is  on  their  meridian  on  the  first  of  June. 

4.  What  inhabitants  of  the  earth  have  their  shadows  directed 
to  every  point  of  the  compass  during  a  revolution  of  the  earth  on 
its  axis  on  the  15th  of  July? 

5.  How  far  does  the  sun  shine  over  the  south  pole  on  the  14th 
of  November,  what  places  in  the  north  frigid  zone  are  in  perpet- 
ual darkness,  and  to  what  places  is  the  sun  vertical  ? 

6.  Find  all  places  of  the  earth  where  the  moon  will  be  vertical 
on  the  3rd  of  June  1825.*. 


PROBLEM  XXIV. 

A  place  being  given  in  the  torrid  zone,  to  find  those  two  days  of  the 
year  on  which  the  sun  will  he  vertical  at  that  plofie. 

Rule.  Bring  the  given  place  to  that  part  of  the  brass  meridian 
which  is  numbered  from  the  equator  towards  the  poles,  and  mark 
its  latitude ;  turn  the  globe  on  its  axis,  and  observe  what  two 
points  of  the  ecliptic  pass  under  that  latitude:  seek  those  points 
of  the  ecliptic  in  the  circle  of  signs  on  the  horizon,  and  exactly 
against  them,  m  the  circle  of  months,  stand  the  days  required. 


*  To  perform  this  example,  find  the  moon's  declination  on  the  given  day  in  the 
Nautical  Almanac,  or  White's  Ephemeris,  and  mark  it  on  the  brass  meridian,  all 
places  passing  under  that  degree  of  declination  will  have  the  moon  vertical,  or 
nearly  so,  on  the  given  day.  The  moon's  declination  at  midnight  on  the  third  of 
June  1825,  is  19^  16'  south. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


211 


Or,  by  the  analemma. 

Find  the  latitude  of  the  given  place  (by  Problem  I.)  and 
mark  it  on  the  brass  meridian ;  bring  the  analemma  to  the  brass 
meridian,  upon  which,  exactly  under  the  latitude,  will  be  found 
the  two  days  required. 

Examples.  1.  On  what  two  days  of  the  year  will  the  sun  be 
vertical  at  Madras  ? 

Answer.  On  the  25th  of  April  and  on  the  18th  of  August. 

2.  On  what  two  days  of  the  year  is  the  sun  vertical  at  the 
following  places. 

Owhyhee  St.  Helena  Sierra  Leone 

Friendly  Isles  Rio  Janeiro  Vera  Cruz 

Straits  of  Alass  Quito  Manilla 

Penang  Barbadoes  Tinian  Isle 

Trincomale  Porto  Bello  Pelew  Islands 


PROBLEM  XXV. 

The  month  and  the  day  of  the  month  being  given  (at  any  place  not 
in  the  frigid  zones),  to  find  what  other  day  of  the  year  is  of  the 
same  length. 

Rule.  Find  the  sun's  place  in  the  ecliptic  for  the  given  day 
(by  Problem  XX.),  bring  it  to  the  brass  meridian,  and  observe 
the  degree  above  it ;  turn  the  globe  on  its  axis  till  some  other 
point  of  the  ecliptic  falls  under  the  same  degree  of  the  meridian  ; 
find  this  point  of  the  ecliptic  on  the  horizon,  and  directly  against 
it  you  will  find  the  day  of  the  month  required. 

This  Problem  may  be  performed  by  the  celestial  globe  in  the  same  manner. 

Or,  by  the  analemma. 

Look  for  the  given  day  of  the  month  on  the  analemma,  and 
adjoining  it  you  will  find  the  required  day  of  the  month. 

Or,  without  a  globe. 

Any  two  days  of  the  year  which  are  of  the  same  length,  will  be 
an  equal  number  of  days  from  the  longest  or  shortest  day.  Hence, 


212 


PROBLEMS  PERFORMED  BY 


Part  III. 


whatever  number  of  days  the  given  day  is  before  the  longest  or 
shortest  day,  just  so  many  days  will  the  required  day  be  after  the 
longest  or  shortest  day,  et  contra. 

Examples.  1.  What  day  of  the  year  is  of  the  same  length  as 
the  25th  of  April  ? 

*inswer.  The  18th  of  August. 

2.  What  day  of  the  year  is  of  the  same  length  as  the  25th  of 
May? 

3.  If  the  sun  rise  at  four  o'clock  in  the  morning  at  London  on 
the  17th  of  July,  on  what  other  day  of  the  year  will  it  rise  at  the 
same  hour? 

4.  If  the  sun  set  at  seven  o'clock  in  the  evening  at  London  on 
the  24th  of  August,  on  what  other  day  of  the  year  will  it  set  at 
the  same  hour? 

5.  If  the  sun's  meridian  altitude  be  90°  at  Trincomale,  in  the 
Island  of  Ceylon,  on  the  12th  of  April,  on  what  other  day  of  the 
year  will  the  meridian  altitude  be  the  same  ? 

6.  If  the  sun's  meridian  altitude  at  London  on  the  25th  of 
April  be  51°  35',  on  what  other  day  of  the  year  will  the  meridian 
altitude  be  the  same  ? 

7.  If  the  sun  be  vertical  at  any  place  on  the  15th  of  April,  how 
many  days  will  elapse  before  he  is  vertical  a  second  time  at  that 
place  ? 

8.  If  the  sun  be  vertical  at  any  place  on  the  20th  of  August, 
how  many  days  will  elapse  before  he  is  vertical  a  second  time  at 
that  place  ? 


PROBLEM  XXVI. 

The  month,  day,  and  hour  of  the  day  being  given,  to  find  where  the 
sun  is  vertical  at  that  instant. 

Rule.  Find  the  sun's  declination  (by  Problem  XX.),  and 
mark  it  on  the  brass  meridian  ;  bring  the  given  place  to  the  brass 
meridian,  and  set  the  .index  of  the  hour-circle  to  twelve  ;  then,  if 
the  given  time  be  before  noon,  turn  the  globe  westward  as  many 
hours  as  it  wants  of  noon ;  but,  if  the  given  time  be  past  noon, 
turn  the  globe  eastward"  ■di^  many  hours  as  the  time  is  past  noon ; 
the  place  exactly  under  the  degree  of  the  sun's  declination  will  be 
that  sought. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


213 


Examples.  1.  When  it  is  forty  minutes  past  six  o'clock  in 
the  morning  at  London  on  the  25th  of  April,  where  is  the  sun 
vertical  ? 

Answer.  Here  the  given  time  is  five  hours  twenty  minutes  before  noon  ;  hence 
the  globe  must  be  turned  towards  the  west  till  the  index  has  passed  over  five  hours 
twenty  minutes,*  and  under  the  sun's  declination  on  the  brass  meridian  you  will 
find  Madras,  the  place  required. 

2.  When  it  is  four  o'clock  in  the  afternoon  at  London  on  the 
18th  of  August,  where  is  the  sun  vertical  ? 

Answer.  Here  the  given  time  is  four  hours  past  noon  ;  hence  the  globe  must  be 
turned  towards  the  east,  till  the  index  has  passed  over  four  hours,  then,  under  the 
sun's  declination,  you  will  find  Barbadoes,  the  place  required. 

3.  When  it  is  three  o'clock  in  the  afternoon  at  London  on  the 
4th  of  January,  where  is  the  sun  vertical  ? 

4.  When  it  is  three  o'clock  in  the  morning  at  London,  on  the 
11th  of  April,  where  is  the  sun  vertical  ? 

5.  When  it  is  thirty  seven  minutes  past  one  o'clock  in  the  af- 
ternoon at  the  Cape  of  Good  Hope  on  the  5th  of  February, 
where  is  the  sun  vertical  ? 

6.  When  it  is  eleven  minutes  past  one  o'clock  in  the  afternoon 
at  London  on  the  29th  of  April,  where  is  the  sun  vertical  ? 

7.  When  it  is  twenty  minutes  past  five  o'clock  in  the  afternoon 
at  Philadelphia  on  the  18th  of  May,  where  is  the  sun  vertical  ? 

8.  When  it  is  nine  o'clock  in  the  morning  at  Calcutta  on  the 
11th  of  April,  where  is  the  sun  vertical? 

PROBLEM  XXVII. 

The  monthy  day,  and  hour  of  the  day  at  any  place  being  given,  to 
find  all  thx)se  places  of  the  earth  where  the  sun  is  rising,  those 
places  where  the  sun  is  setting,  those  places  that  have  noon,  that 
particular  place  where  the  sun  is  vertical,  those  places  that  have 
morning  twilight,  those  places  that  have  evening  twilight,  and 
those  places  that  have  midnight. 

Rule.  Find  the  sun's  declination  (by  Problem  XX.)  and  mark 
it  on  the  brass  meridian  ;  elevate  the  north  or  south  pole,  accord- 


+  If  the  hour  circle  be  not  divided  to  twenty  minutes,  turn  the  globe  westward 
till  the  index  has  passed  over  five  hours  and  a  quarter  ;  then,  by  turning  it  a  degree 
and  a  quarter  farther  to  the  west  (answering  to  five  minutes  of  time),  the  solution 
will  be  exact.  See  the  note  to  the  next  Problem.  The  degrees  must  be  counted 
on  the  equator. 


214 


PROBLEMS  PERFORMED  BY 


Part  III. 


ing  as  the  sun's  declination  is  north  or  south,  so  many  degress 
above  the  horizon  as  are  equal  to  the  sun's  declination ;  bring 
the  given  place  to  the  brass  meridian,  and  set  the  index  of  the 
hour  circle  to  twelve  ;  then,  if  the  given  time  be  before  noon,  turn 
the  globe  westward  as  many  hours  as  it  wants  of  noon ;  but,  if  the 
given  time  be  past  noon,  turn  the  globe  eastward  as  many  hours 
as  the  time  is  past  noon  :  keep  the  globe  in  this  position ;  then 
all  places  along  the  western  edge  of  the  horizon  have  the  sun 
rising  ;  those  places  along  the  eastern  edge  have  the  sun  setting  ; 
those  under  the  brass  meridian  above  the  horizon,  have  noon ; 
that  particular  place  which  stands  under  the  sun's  declination  on 
the  brass  meridian,  has  the  sun  vertical :  all  places  below  the 
western  edge  of  the  horizon,  within  eighteen  degrees,  have  morn- 
ing twilight ;  those  places  which  are  below  the  eastern  edge  of 
the  horizon,  within  eighteen  degrees,  have  evening  twilight ;  all 
places  under  the  brass  meridian  below  the  horizon,  have  midnight ; 
all  the  places  above  the  horizon  have  day,  and  those  below  it  have 
night  or  tw^ilight. 

Examples.  1.  When  it  is  fifty-two  minutes  past  four  o'clock 
in  the  morning  at  London  on  the  5th  of  March,  find  all  places  of 
the  earth  where  the  sun  is  rising,  setting,  &c.  &c. 

Answer.  The  sun's  declination  will  be  found  to  be  65°  south ;  therefore,  elevate 
the  south  pole  above  the  horizon.  The  given  time  being  seven  hours  eight 
minutes  before  noon  (=  I2h. — 4h,  52m.)  the  globe  must  be  turned  towards  the 
west,  till  the  index  has  passed  over  seven  hours  eight  minutes.*  Let  the  globe  be 
fixed  in  this  position  ;  then, 

The  sun  is  rising  at  the  western  part  of  the  White  Sea,  Petersburg,  Morea  in 
Turkey,  &c. 

.  Setting  at  the  eastern  coast  of  Kamtschatka,  Jesus  Island,  Palmerston  Island, 
&c.  between  the  Friendly  and  Society  Islands. 

JVbon  at  the  late  Baikal  in  Irkoutsk,  Cochin  China,  Cambodia,  Sunda  Islands,  &c. 
Vertical  at  Batavia. 

Morning  twilight  at  Sweden,  part  of  Germany,  the  southern  part  of  Italy,  Sicily, 
the  western  coast  of  Africa  along  the  ^thiopean  Ocean,  &c. 

Evening  twilight  at  the  north  west  extremity  of  North  America,  the  Sandwich 
Islands,  Society  Islands,  &c. 

Midnight  at  Labrador,  New- York,  western  part  of  St.  Domingo,  Chili,  and  the 
western  coast  of  South  America. 

Day  at  the  eastern  part  of  Russia  in  Europe,  Turkey,  Egypt,  the  Cape  of  Good 
Hope,  and  all  the  eastern  part  of  Africa,  almost  the  whole  of  Asia,  &c. 


*  The  hour-circles,  in  general,  are  not  divided  into  parts  less  than  a  quarter  of 
an  hour,  but  the  odd  minutes  are  easily  reckoned.  In  this  example,  having  turned 
the  globe  westward  till  the  index  has  passed  over  seven  hours ;  then,  because  four 
minutes  of  time  make  one  degree,  reckon  tioo  degrees  on  the  equator  eastward, 
and  turn  the  globe  till  they  pass  under  the  brass  meridian. 


Chap,  I. 


THE  TERRESTRIAL  GLOBE. 


215 


J^ight  at  the  whole  of  North  and  South  America,  the  western  part  of  Africa,  the 
British  Isles,  France,  Spain,  Portugal,  &c. 

2.  When  it  is  four  o'clock  in  the  afternoon  at  London  on  the 
25th  of  April,  where  is  the  sun  rising,  setting,  &c.  &c.  ? 

Answer.  The  sun's  declination  being  13°  north,  the  north  pole  must  be  elevated 
13°  above  the  horizon*;  and  as  the  given  time  is  four  o'clock  in  the  afternoon,  the 
globe  must  be  turned  four  hours  towards  the  east;  then  the  sun  will  be  rising  at 
Owhyhee,  &c.  setting  at  the  Cape  of  Good  Hope,  &c,;  it  will  be  noon  at  Buenos 
Ayres,  &c.  the  sun  will  be  vertical  at  Barbadoes,  and,  following  the  directions  in  the 
Problem,  all  the  other  places  are  readily  found. 

3.  When  it  is  ten  o'clock  in  the  morning  at  London  on  the 
longest  day,  to  what  countries  is  the  sun  rising,  setting,  <fec.  &:c.? 

4.  When  it  is  ten  o'clock  in  the  afternoon  at  Botany  Bay  on  the 
15th  of  October,  where  is  the  sun  rising,  setting,  &c.  &c. 

5.  When  is  it  seven  o'clock  in  the  morning  at  Washington  on 
the  17th  of  February,  where  is  the  sun  rising,  setting,  &c.  &c.? 

6.  When  it  is  midnight  at  the  Cape  of  Good  Hope  on  the  27th 
of  July,  where  is  the  sun  rising,  setting,  &c.  &c. 


PROBLEM  XXVIII. 

To  find  the  time  of  the  sun's  rising  and  setting,  and  length  of  th^ 
day  and  night,  at  any  place  not  in  the  frigid  zones. 

Rule.  Find  the  sun's  declination  (by  Problem  XX.)  and  ele- 
vate the  north  or  south  pole,  according  as  the  declination  is  north 
or  south,  so  many  degrees  above  the  horizon  as  are  equal  to  the 
sun's  declination ;  bring  the  given  place  to  the  brass  meridian, 
and  set  the  index  of  the  hour-circle  to  twelve ;  turn  the  globe 
eastward  till  the  given  place  comes  to  the  eastern  semi-circle  of 
the  horizon,  and  the  number  of  hours  passed  over  by  the  index 
will  be  the  time  of  the  sun's  setting :  deduct  these  hours  from 
twelve,  and  you  have  the  time  of  the  sun's  rising ;  because  the 
sun  rises  as  many  hours  before  twelve  as  it  sets  after  twelve. 
Double  the  time  of  the  sun's  setting  gives  the  length  of  the  day, 
and  double  the  time  of  rising  gives  the  length  of  the  night. 

By  the  same  rule,  the  length  of  the  longest  day,  at  all  places  not  in  the  frigid  zones, 
may  be  readily  found ;  for  the  longest  day  at  all  places  in  north  latitude  is  on  the 
21st  of  June,  or  when  the  sun  enters  Cancer ;  and  the  longest  day  at  all  places  in 


*  If  the  hour-circle  of  the  globe  be  placed  above  the  brass  meridian,  it  must  be 
unscrewed  and  removed  from  the  pole  j  the  hours  may  then  be  counted  on  the 
equator.   See  the  note*  to  definition  19.  p.  29. 


216 


PROBLEMS  PERFORMED  BY 


Part  III. 


south  latitude  is  on  the  21st  of  December,  or  when  the  sun  enters  the  sign  of  Cap- 
ricorn. 

Or, 

Find  the  latitude  of  the  given  place,  and  elevate  the  north  or 
south  pole,  according  as  the  latitude  is  north  or  south,  so  many 
degrees  above  the  horizon  as  are  equal  to  the  latitude ;  find  the 
sun's  place  in  the  ecliptic  (by  Problem  XX.),  bring  it  to  the  brass 
meridian,  and  set  the  index  of  the  hour  circle  to  twelve ;  turn  the 
globe  westward  till  the  sun's  place  comes  to  the  western  semi- 
circle of  the  horizon,  and  the  number  of  hours  passed  over  by  the 
index  will  be  the  time  of  the  sun's  setting ;  and  these  hours  taken 
from  twelve  will  give  the  time  of  rising ;  then,  as  before,  double 
the  time  of  setting,  gives  the  length  of  the  day,  and  double  the 
time  of  rising,  gives  the  length  of  the  night. 

Or,  by  the  analemma. 

Find  the  latitude  of  the  given  place,  and  elevate  the  north  or 
south  pole,  according  as  the  latitude  is  north  or  south,  the  same 
^  number  of  degrees  above  the  horizon  ;  bring  the  middle  of  the 
analemma  to  the  brass  meridian,  and  set  the  index  of  the  hour- 
circle  to  twelve  ;  turn  the  globe  westward  till  the  day  of  the  month 
on  the  analemma  comes  to  the  western  semi-circle  of  the  hori- 
zon, and  the  number  of  hours  passed  over  by  the  index  will  be 
the  time  of  the  sun's  setting,  &c.  as  above. 

Examples.  What  time  does  the  sun  rise  and  set  at  London 
on  the  1st  of  June,  and  what  is  the  length  of  the  day  and  night? 

S.nswer.  The  sun  sets  at  8  min.  past  8,  and  rises  at  52  min.  past  3,  the  length 
of  the  day  is  6  hours  16  minutes,  and  the  length  of  the  night  7  hours  44  minutes. 
The  learner  will  readily  perceive  that  if  the  time  at  which  the  sun  rises  be  given,  the 
time  at  which  it  sets,  together  with  the  length  of  the  day  and  night,  may  be  found 
without  a  globe ;  if  the  length  of  the  day  be  given,  the  length  of  the  night  and  the 
time  the  sun  rises  and  sets  may  be  found  ;  if  the  length  of  the  night  be  given,  the 
length  of  the  day  and  the  time  the  sun  rises  and  sets  are  easily  known. 

2.  At  what  time  does  the  sun  rise  and  set  at  the  following 
places,  on  the  respective  days  mentioned,  and  what  is  the  length 
of  the  day  and  night  ? 


London,  17th  of  May 
Gibraltar,  22d  of  July 
Edinburgh,  29th  January 
Botany  Bay,  20th  February 
Pekin  20th  of  April 


Cape  of  Good  Hope,  7  Dec. 
Cape  Horn,  29th  January 
Washington,  15th  December 
Petersburg,  24th  October 
Constantinople,  18th  Aug. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


217 


3.  Find  the  time  the  sun  rises  and  sets  at  every  place  on  the 
surface  of  the  globe  on  the  21st  of  March,  and  likewise  on  the 
23d  of  September. 

4.  Required  the  length  of  the  longest  day  and  shortest  night  at 
the  following  places : 

London  Paris  Pekin 

Petersburg  Vienna  Cape  Horn 

Aberdeen  Berlin  Washington 

Dublin  Buenos  Ayres  Cape  of  Good  Hope 

Glasgow  Botany  Bay  Copenhagen. 

5.  Required  the  length  of  the  shortest  day  and  longest  night  at 
the  following  places : 

London  Lima  P^ris 

Archangel  Mexico  l|(8whyhee 

O  Taheitee  St.  Helena  Lisbon 

Que^lll^  Alexandria  Falkland  Islands. 

6.  How  much  longer  is  the  21st  of  June  at  Petersburg  than  at 
afeUexandria  ? 

7.  How  much  longer  is  the  21st  of  December  at  Alexandria 
than  at  Petersburg  ? 

8.  At  what  time  does  the  sun  rise  and  set  at  Spitzbergen  on 
the  5th  of  April? 


PROBLEM  XXIX. 


The  length  of  the  day  at  any  place,  not  in  the  frigid  zones,  being 
given,  to  find  the  suns  declination  and  the  day  of  the  month. 

Rule.  Bring  the  given  place  to  the  brass  meridian,  and  set 
the  index  to  twelve :  turn  the  globe  eastward  till  the  index  has 
passed  over  as  many  hours  as  are  equal  to  half  the  length  of  the 
day ;  keep  the  globe  from  revolving  on  its  axis,  and  elevate  or 
depress  one  of  the  poles  till  the  given  place  exactly  coincides  with 
the  eastern  semi-circle  of  the  horizon  ;  the  distance  of  the  elevated 
pole  from  the  horizon  will  be  the  sun's  declination :  mark  the 
sun's  declination,  thus  found,  on  the  brass  meridian:  turn  the 
globe  on  its  axis,  and  observe  what  two  points  of  the  ecliptic  pass 
under  this  mark ;  seek  those  points  in  the  circle  of  signs  on  the 
horizon,  and  exactly  against  them,  in  the  circle  of  months,  stand 
the  days  of  the  months  required. 

28 


218 


PROBLEMS  PERFORMED  BY 


Part  III. 


Or, 

Bring  the  meridian  passing  through  Libra^  to  coincide  with  the 
brass  meridian,  elevate  the  pole  to  the  latitude  of  the  place,  and 
set  the  index  of  the  hour-circle  to  twelve  ;  turn  the  globe  east- 
ward till  the  index  has  passed  over  as  many  hours  as  are  equal  to 
half  the  length  of  the  day,  and  mark  where  the  meridian  passing 
through  Libra  is  cut  by  the  eastern  semi-circle  of  the  horizon  ; 
bring  this  mark  to  the  brass  meridian,-]-  and  the  degree  above  it 
is  the  sun's  declination ;  with  which  proceed  as  above. 

Or,  by  the  analemma. 


Bring  the  middle  of  the  analemma  to  the  brass  meridian,  ele- 
vate the  pole  to  the  latitude  of  the  place,  and  set  tlj^|dex  of  the 
hour-circle  to  twelve  ;  turn  the  globe  eastward  till^^Wndex  has 
passed  over  as  many  hours  as  are  equal  to  half  the  length  of  tl^g^ 
day ;  the  two  days,  on  the  analemma,  which  are  cut  by  the  eas^^ 
ern  semi-circle  of  the  horizon,  will  be  the  days  required  ;  and,  by 
bringing  the  analemma  to  the  brass  meridian,  the  sun's  declina- 
tion will  stand  exactly  above  these  days. 

Examples.    1.  What  two  days  in  the  year  are  each  sixteen 
hours  long  at  London,  and  what  is  the  sun's  declination  ? 

Answer.    The  24th  of  May  and  the  17th  of  July.    The  sun's  declination  is 
about  21°  north. 

2.  What  two  days  of  the  year  are  each  fourteen  hours  long  at 
London  ? 

3.  On  what  two  days  of  the  year  does  the  sun  set  at  half-past 
seven  o'clock  at  Edinburgh  ? 

4.  On  what  two  days  of  the  year  does  the  sun  rise  at  four 
o'clock  at  Petersburg  ? 

5.  What  two  nights  of  the  year  are  each  ten  hours  long  at 
Copenhagen  ? 

6.  What  day  of  the  year  at  London  is  sixteen  hours  and  a  half 
long? 


*  Any  meridian  will  answer  the  purpose,  and  the  globe  may  be  turned  either 
eastward  or  westward ;  but  it  is  the  most  convenient  to  turn  it  eastward,  beca.use 
the  brass  meridian  is  graduated  on  the  east  side. 

t  If  Adams'  globes  be  used,  the  meridian  passing  through  Libra  is  graduated  like 
the  brass  meridian,  and  the  declination  is  found  at  onee. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE, 


219 


PROBLEM  XXX. 

To  find  the  length  of  the  longest  day  at  any  place  in  the  north* 

frigid  lone. 

Rule.    Bring  the  given  place  to  the  northern  point  of  the 
horizon  (by  elevating  or  depressing  the  pole),  and  observe  its 
distance  from  the  north  pole  on  the  brass  meridian ;  count  the 
same  number  of  degrees  on  the  brass  meridian  from  the  equator, 
towards  the  north  pole,  and  mark  the  place  where  the  reckoning 
ends  :  turn  the  globe  on  its  axis,  and  observe  what  two  points  of 
the  ecliptic  pass  under  the  above  mark  ;  find  those  points  of  the 
ecliptic  in  the  circle  of  signs  on  the  horizon,  and  exactly  against 
them,  in  the  circle  of  months,  you  will  find  the  days  on  which  the 
longest  (^^A|^ins  and  ends.    The  day  preceding  the  21st  of 
^^e  is  tn^^n  which  the  longest  day  begins  at  the  given  place, 
wKi  the  day  following  the  21st  of  June  is  that  on  which  the 
Tongest  day  ends :  the  time  between  these  days  is  the  length  of 
the  longest  day. 

Or,  by  the  analemma. 

Bring  the  given  place  to  that  part  of  the  brass  meridian  which 
is  numbered  from  the  north  pole  towards  the  equator,  and  observe 
its  distance  in  degrees  from  the  pole ;  count  the  same  number  of 
degrees  on  the  brass  meridian  from  the  equator  towards  the  north 
pole,  and  mark  where  the  reckoning  ends  ;  bring  the  analemma 
to  the  brass  meridian,  and  the  two  days  which  stand  under  the 
above  mark  will  point  out  the  beginning  and  end  of  the  longest 
day. 

Examples.  1.  What  is  the  length  of  the  longest  day  at  the 
North  Cape,  in  the  island  of  Maggeroe,  in  latitude  71°  30'  north? 

Answer.  The  place  is  18^°  from  the  pole ;  the  longest  day  begins  on  the  14th  of 
May,  and  ends  on  the  30th  of  July  ;  the  day  is  therefore  seventy-seven  days  long, 
that  is,  the  sun  does  not  set  during  seventy- seven  revolutions  of  the  earth  on  its  axis. 

2.  What  is  the  length  of  the  longest  day  in  the  north  of  Spitz- 
bergen,  and  on  what  day  does  it  begin  and  end  ? 


+  The  south  frigid  zone  being  uninhabited  (at  least  we  know  of  no  inhabitants) 
the  Problem  is  not  appUed  to  that  zone ;  however,  the  rule  is  general,  reading 
south  for  north,  and  21st  of  December  for  the  2l9t  of  June. 


220 


PROBLEMS  PERFORMED  BY 


Part  III. 


3.  What  is  the  length  of  the  longest  day  at  the  northern 
extremity  of  Nova  Zernbla  ? 

4.  What  is  the  length  of  the  longest  day  at  the  north  pole,  and 
on  what  day  does  it  begin  and  end  ? 

PROBLEM  XXXI. 

To  find  the  length  of  the  longest  night  at  any  place  in  the  north^ 

frigid  zone. 

Rule.  Bring  the  given  place  to  the  northern  point  of  the 
horizon  (by  elevating  or  depressing  the  pole),  and  observe  its 
distance  from  the  north  pole  on  the  brass  meridian  ;  count  the 
same  number  of  degrees  on  the  brass  meridian  from  the  equator 
towards  the  south  pole,  and  mark  the  place  where  the  reckoning 
ends  ;  turn  the  globe  on  its  axis,  and  observe  what  two  points  of 
the  ecliptic  pass  under  the  above  mark ;  find  thos^Aints  of  the 
echptic  in  the  circle  of  signs  on  the  horizon,  and  exWff)  against 
them  in  the  circle  of  months,  you  will  find  the  days  on  which  thel| 
longest  night  begins  and  ends.  The  day  preceding  the  2ist  o^ 
December  is  that  on  which  the  longest  night  begins  at  the  given 
place,  and  the  day  following  the  21st  of  December  is  that  on  which 
the  longest  night  ends  :  the  time  between  these  days  is  the  length 
of  the  longest  night. 

Or,  by  the  analemma. 

Bring  the  given  place  to  that  part  of  the  brass  meridian  which 
is  numbered  from  the  north  pole  towards  the  equator,  and  observe 
its  distance  in  degrees  from  the  pole  ;  count  the  same  number  of 
degrees  on  the  brass  meridian  from  the  equator  towards  the  south 
pole,  and  mark  where  the  reckoning  ends  ;  bring  the  analemma  to 
the  brass  meridian,  and  the  two  days  which  stand  under  the  above 
mark  will  point  out  the  beginning  and  end  of  the  longest  night. 

Examples.  1.  What  is  the  length  of  the  longest  night  at  the 
North  Cape,  in  the  island  of  Maggeroe,  in  latitude  71°  30'  north  ? 

Answer.  The  place  is  18^°  from  the  pole  ;  the  longest  night  begins  on  the  16th 
of  November,  and  ends  on  the  27th  of  January:  the  night  is  therefore  seventy- 
three  days  long,  that  is,  the  sun  does  not  rise  during  seventy-three  revolutions  of 
the  earth  on  its  axis. 


*  This  Problem  is  equally  applicable  to  any  place  in  the  south  frigid  zone,  and 
the  rule  will  be  general  by  reading  south  for  north,  and  the  contrary ;  likewise, 
instead  of  the  21st  of  December  read  the  21st  of  June. 


Chap.  1. 


THE  TERRESTRIAL  GLOBE. 


221 


2.  What  is  the  length  of  the  longest  night  at  the  north  of 
Spitzbergen  ? 

3.  The  Dutch  wintered  in  Nova  Zembla,  latitude  76  degrees 
north,  in  the  year  1596 ;  on  what  day  of  the  month  did  they  lose 
sight  of  the  sun  ;  on  what  day  of  the  month  did  he  appear  again  ; 
and  how  many  days  were  they  deprived  of  his  appearance,  set- 
ting aside  the  effect  of  his  refraction  ? 

4.  For  how  many  days  are  the  inhabitants  of  the  northernmost 
extremity  of  Russia  deprived  of  a  sight  of  the  sun  ? 

PROBLEM  XXXII. 

To  find  the  number  of  days  which  the  sun  rises  and  sets  at  any 
place  on  the  north^  frigid  zone. 

Rule.  Bring  the  given  place  to  the  northern  point  of  the  hori- 
zon (by  elevating  or  depressing  the  pole),  and  observe  its  dis- 
tance from  the  north  pole  on  the  brass  meridian  ;  count  the  same 
number  of  degrees  on  the  brass  meridian  from  the  equator  towards 
the  poles  northward  and  southward,  and  make  marks  where  the 
reckoning  ends ;  observe  what  two  points  of  the  ecliptic  nearest 
to  Aries  pass  under  the  above  marks  ;  these  points  will  show  (upon 
the  horizon)  the  end  of  the  longest  night  and  the  beginning  of  the 
longest  day  ;  during  the  time  between  these  days  the  sun  will  rise 
and  set  every  twenty-four  hours  ;  next  observe  what  two  points 
of  the  ecliptic  nearest  to  Libra,  pass  under  the  marks  on  the  brass 
meridian ;  find  these  points,  as  before,  in  the  circle  of  signs,  and 
against  them  you  will  find  the  day  on  which  the  longest  night  be- 
gins ;  during  the  time  between  these  days  the  sun  will  rise  and 
set  every  twenty-four  hours. 

Or, 

Find  the  length  of  the  longest  day  at  the  given  place  (by  Prob. 
XXX.)  and  the  length  of  the  longest  night  (by  Prob.  XXXI),  add 
these  together,  and  subtract  the  sum  from  365  days,  the  length  of 
the  year,  the  remainder  will  show  the  number  of  days  which  the 
sun  rises  and  sets  at  that  place. 


*  The  same  might  be  found  for  a  place  in  the  south  frigid  zone,  were  that  25one 
inhabited. 


222 


PROBLEMS  PERFORMED  BY 


Part  III. 


Or,  by  the  analemma. 

Find  how  many  degrees  the  given  place  is  from  the  north  pole, 
and  mark  those  degrees  upon  the  brass  meridian  on  both  sides  of 
the  equator ;  observe  what  four  days  on  the  analemma  stand  under 
the  marks  on  the  brass  meridian ;  the  time  between  those  two 
days  on  the  left-hand  part  of  the  analemma  (reckoning  towards 
the  north  pole)  will  be  the  number  of  days  on  which  the  sun  rises 
and  sets,  between  the  end  of  the  longest  night  and  the  beginning 
of  the  longest  day :  and  the  time  between  the  two  days  on  the 
right-hand  part  of  the  analemma  (reckoning  towards  the  south 
pole)  will  be  the  number  of  days  on  which  the  sun  rises  and  sets, 
between  the  end  of  the  longest  day  and  the  beginning  of  the  long- 
est night. 

Examples.  1.  How  many  days  in  the  year  does  the  sun  rise 
and  set  at  the  North  Cape,  in  the  island  of  Maggeroe,  in  latitude 
71° 30' north? 

Answer.  The  place  is  18J«>  from  the  pole,  the  two  points  in  the  ecliptic,  nearest 
to  Aries  J  which  pass  under  18^°  on  the  brass  meridian,  are  8°  in  answering  to 
the  27th  of  January,  and  24°  in  ^ ,  answering  the  14th  of  May.  Hence  the  sun 
rises  and  sets  for  107  days,  viz.  from  the  end  of  the  longest  night,  which  happens  on 
the  27th  of  January,  to  the  beginning  of  the  longest  day,  which  happens  on  the 
14th  of  May.  Secondly,  the  two  points  in  the  ecliptic  nearest  to  Libra,  which  pass 
under  18|p  on  the  brass  meridian,  are  8°  in  Q,,  answering  to  the  30th  of  July,  and 
24°  in  Til,  answering  to  the  1 5th  of  November.  Hence  the  sun  rises  and  sets  for 
108  days,  viz.  from  the  end  of  the  longest  day,  which  happens  on  the  30th  of  July, 
to  the  beginning  of  the  longest  night,  which  happens  on  the  15th  of  November; 
so  that  the  whole  time  of  the  sun's  rising  and  setting  is  215  days. 

Or,  thus  : 

The  length  of  the  longest  day,  by  Example  1st.  Prob  XXX,  is  77  days  ;  the 
length  of  the  longest  night,  by  Example  1st,  Prob.  XXXI.  is  73  days;  the  sum  of 
these  is  150,  which  deducted  from  365,  leaves  215  days  as  above. 

2.  How  many  days  in  the  year  does  the  sun  rise  and  set  at  the 
north  of  Spitzbergen  ? 

3.  How  many  days  does  the  sun  rise  and  set  at  Greenland,  in 
latitude  75° north? 

4.  How  many  days  does  the  sun  rise  and  set  at  the  northern 
extremity  of  Russia  in  Asia  ? 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


223 


PROBLEM  XXXIII. 

To  find  in  what  degree  of  north  latitude,  on  any  day  between  the 
2lst  of  March  and  2lst  of  June,  or  in  what  degree  of  south 
latitude,  on  any  day  between  the  23<i  of  September  and  the  ^Vst 
of  December,  the  sun  begins  to  shine  constantly  without  setting; 
and  also  in  what  latitude  in  the  opposite  hemisphere  he  begins  to 
be  totally  absent. 

Rule.  Find  the  sun's  declination  (by  Problem  XX.),  and 
count  the  same  number  of  degrees  from  the  north  pole  towards  the 
equator,  if  the  declination  be  north,  or  from  the  south  pole,  if  it  be 
south,  and  mark  the  point  where  the  reckoning  ends :  turn  the 
globe  on  its  axis,  and  all  places  passing  under  this  mark  are  those 
in  which  the  sun  begins  to  shine  constantly  without  setting  at  that 
time :  the  same  number  of  degrees  from  the  contrary  pole  will 
point  out  all  the  places  where  twilight  or  total  darkness  begins. 

Examples.  I.  In  what  latitude  north,  and  at  what  places,  does 
the  sun  begin  to  shine  without  setting  during  several  revolutions 
of  the  earth  on  its  axis,  on  the  14th  of  May  ? 

Answer.  The  sun's  declination  is  18^°  north,  therefore  all  places  in  latitude  71^° 
north,  will  be  the  places  sought,  viz.  the  North  Cape  in  Lapland,  the  southern  part 
of  Nova  Zembla,  Icy  Cape,  &c. 

2.  In  what  latitude  south  does  the  sun  begin  to  shine  without 
setting  on  the  I8th  of  October,  and  in  what  latitude  north  does  he 
begin  to  be  totally  absent  ? 

Answer.  The  sun's  declination  is  10°  south,  therefore  he  begins  to  shine  con- 
stantly in  latitude  80°  south,  where  there  are  no  inhabitants  known,  and  to  be  to- 
tally absent  in  latitude  80°  north,  viz.  at  Spitzbergen. 

3.  In  what  latitude  does  the  sun  begin  to  shine  without  setting 
on  the  20th  of  April? 

4.  In  what  latitude  north  does  the  sun  begin  to  shine  without 
setting  on  the  1st  of  June,  and  in  what  degree  of  south  latitude 
does  he  begin  to  be  totally  absent  ? 

PROBLEM  XXXIV. 

Any  number  of  days,  not  exceeding  182,  being  given,  to  find  the 
parallel  of  north  latitude  in  which  the  sun  does  not  set  for  that 
time. 

Rule.  Count  half  the  number  of  days  from  the  21st  of  June 
on  the  horizon,  eastward  or  westward,  and  opposite  to  the  last  day 


224 


PROBLEMS  PERFORMED  BY 


Part  III. 


you  will  find  the  sun's  place  in  the  circle  of  signs :  look  for  the 
sign  and  degree  on  the  ecliptic,  which  bring  to  the  brass  merid- 
ian, and  observe  the  sun's  decHnation ;  reckon  the  same  number 
of  degrees  from  the  north  pole  (on  that  part  of  the  brass  meridian 
which  is  numbered  from  the  equator  towards  the  poles)  and  you 
will  have  the  latitude  sought. 

Examples.  1.  In  what  degree  of  north  latitude,  and  at  what 
place  does  the  sun  continue  above  the  horizon  for  seventy-seven 
days  ? 

Jlnsv)er.  Half  the  number  of  days  is  38^,  and  if  reckoned  backward,  or  towards 
the  east,  from  the  21st  of  June,  will  answer  to  the  14th  of  May  ;  and  if  counted  for- 
ward, or  towards  the  west,  will  answer  to  the  30th  of  July ;  on  either  of  which  days 
the  sun's  declination  is  18^  degrees  north,  consequently  the  places  sought  are  18^ 
degrees  from  the  north  pole,  or  in  latitude  71^  degrees  north ;  answering  to  the 
North  Cape  in  Lapland,  the  south  part  of  Nova  Zembla,  Icy  Cape,  &c. 

2.  In  what  degree  of  north  latitude  is  the  longest  day  134  days, 
or  3216  hours  in  length  ? 

3.  In  what  degree  of  north  latitude  does  the  sun  continue  above 
the  horizon  for  2160  hours  ? 

4.  In  what  degree  of  north  latitude  does  the  sun  continue  above 
the  horizon  for  1152  hours  ? 


PROBLEM  XXXV. 

To  find  the  heginningy  end,  and  duration  of  twilight  at  any  place 
on  any  given  day. 

Rule.  Find  the  sun's  declination  for  the  given  day  (by  Prob- 
lem XX.),  and  elevate  the  north  or  south  pole,  according  as  the 
declination  is  north  or  south,  so  many  degrees  above  the  horizon 
as  are  equal  to  the  sun's  declination ;  screw  the  quadrant  of  alti- 
tude on  the  brass  meridian,  over  the  degree  of  the  sun's  declina- 
tion ;  bring  the  given  place  to  the  brass  meridian,  and  set  the  in- 
dex of  the  hour-circle  to  twelve  ;  turn  the  globe  eastward  till  the 
given  place  comes  to  the  horizon,  and  the  hours  passed  over  by 
the  index,  will  show  the  time  of  the  sun's  setting,  or  the  beginning 
of  evening  twilight :  continue  the  motion  of  the  globe  eastward, 
till  the  given  place  coincides  with  18°  on  the  quadrant  of  altitude 
below*  the  horizon,  and  the  hours  passed  over  by  the  index,  from 


*  The  quadrant  of  altitude  belonging  to  our  modern  globes  is  always  graduated 
to  18  degrees  below  the  horizon. 


Chap,  L 


THE  TERRESTRIAL  GLOBE. 


225 


12,  will  show  when  evening  twilight  ends.  The  time  when 
evening  twilight  ends,  subtracted  from  12,  will  show  the  beginning 
of  morning  twilight. 

Or  thus  : 

Elevate  the  north  or  south  pole,  according  as  the  latitude  of  the 
given  place  is  north  or  south,  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  ;  find  the  sun's  place  in  the  ecliptic, 
bring  it  to  the  brass  meridian,  set  the  index  of  the  hour-circle  to 
twelve,  and  screw  the  quadrant  of  altitude  upon  the  brass 
meridian  over  the  given  latitude  ;  turn  the  globe  westward  on  its 
axis  till  the  sun's  place  comes  to  the  western  edge  of  the  horizon, 
and  the  hours  passed  over  by  the  index  will  show  the  time  of  the 
sun's  setting,  or  the  beginning  of  evening  twilight ;  continue  the 
motion  of  the  globe  westward  till  the  sun's  place  coincides  with 
11°  on  the  quadrant  of  altitude  below  the  horizon,  the  time 
passed  over  by  the  index  of  the  hour-circle,  from  the  time  of  the 
sun's  setting,  will  show  the  duration  of  evening  twilight. 

Or,  by  the  analemma. 

Elevate  the  pole  to  the  latitude  of  the  place,  as  above,  and 
screw  the  quadrant  of  altitude  upon  the  brass  meridian  over  the 
degree  of  latitude  ;  bring  the  middle  of  the  analemma  to  the 
brass  meridian,  and  set  the  index  of  the  hour-circle  to  twelve  ; 
turn  the  globe  westward  till  the  given  day  of  the  month,  on  the 
analemma,  comes  to  the  western  edge  of  the  horizon,  and  the 
hours  passed  over  by  the  index  will  show  the  time  of  the  sun's 
setting,  or  the  beginning  of  evening  twilight :  continue  the  motion 
of  the  globe  westward  till  the  given  day  of  the  month  coincides 
with  18^  on  the  quadrant  below  the  horizon,  the  time  passed  over 
by  the  index,  from  the  time  of  the  sun's  setting,  will  show  the 
duration  of  evening  twilight. 

Examples.  1.  Required  the  beginning,  end,  and  duration  of 
morning  and  evening  twilight  at  London,  on  the  19th  of  April. 

Answer.  The  sun  sets  at  two  minutes  past  seven,  and  evening  twilight  ends  at 
nineteen  minutes  past  nine;  consequently  morning  twilight  begins  at  (12 h. — 
9h.  19m.=)2h.  41m.  and  ends  at  (12  h.— 7  h.  2m. =)  4  h.  58m.;  the  duration 
of  twilight  is  2  h.  and  17  minutes. 

2.  What  is  the  duration  of  twilight  at  London  on  the  23d  of 
September?  what  time  does  dark  night  begin,  and  at  what  time 
does  the  day-break  in  the  morning  ? 

Answer,  The  sun  sets  at  six  o'clock,  and  the  duration  of  twilight  is  two  hours  ; 
consequently  the  evening  twilight  ends  at  eight  o'clock,  and  the  morning  twilight 
begins  at  four. 

29 


220 


PROBLEMS  PERFORMED  BY 


Part  IIL 


3.  Required  the  beginning,  end,,  and  duration  of  morning  and 
evening  twilight  at  London  on  the  25th  of  August. 

4.  Required  the  beginning,  end,  and  duration  of  morning  and 
evening  twilight  at  Edinburgh  on  the  20th  of  February. 

5.  Required  the  beginning,  end,  and  duration  of  morning  and 
evening  twilight  at  Cape  Horn  on  the  20th  of  February. 

6.  Required  the  beginning,  end,  and  duration  of  morning  and 
evening  twilight  at  Madras  on  the  15th  of  June. 


PROBLEM  XXXVL 

To  find  the  beginning,  end,  and  duration  of  constant  day  or  twilight 

at  any  place. 

Rule.  Find  the  latitude  of  the  given  place,  and  add  18°  to  that 
latitude  ;  count  the  number  of  degrees  correspondent  to  the  sum, 
on  that  part  of  the  brass  meridian  which  is  numbered  from  the 
pole  towards  the  equator,  mark  where  the  reckoning  ends,  and 
observe  what  two  points  of  the  ecliptic  pass  under  the  mark  ;* 
that  point  wherein  the  sun's  declination  is  increasing  will  show 
on  the  horizon  the  beginning  of  constant  twilight ;  and  that  point 
wherein  the  sun's  declination  is  decreasing,  will  show  the  end  of 
constant  twilight. 

Examples.  1.  When  do  we  begin  to  have  constant  day  or 
twilight  at  London,  and  how  long  does  it  continue  ? 

Answer.  The  latitude  of  London  is  51 J  degrees  north,  to  which  add  18  degrees, 
the  sum  is  69^,  the  two  points  of  the  ecliptic  which  pass  under  69^  are  two  degrees 
in  n>  answering  to  the  22d  of  May.  and  29  degrees  in  ^d?  answering  to  the  21st  of 
July  ;  so  that,  from  the  22d  of  May  tiD  the  21st  of  July  the  sun  never  descends  18 
degrees  below  the  horizon  of  London. 

2.  When  do  the  inhabitants  of  the  Shetland  Islands  cease  to 
have  constant  day  or  twilight  ? 

3.  Can  twilight  ever  continue  from  sun-set  to  sun-rise  at 
Madrid  ? 

4.  When  does  constant  day  or  twilight  begin  at  Spitzbergen  ? 

5.  What  is  the  duration  of  constant  day  or  twilight  at  the 
North  Cape  in  Lapland,  and  on  what  day,  after  their  long  winter's 
night,  do  the  sun's  rays  first  enter  the  atmosphere  ? 


*  If,  after  IS  degrees  be  added  to  the  latitude,  the  distance  from  the  pole  will 
not  reach  the  ecHptic,  there  will  be  no  constant  twilight  at  the  given  place, 
viz.  to  the  given  latitude  add  18  degrees,  and  subtract  the  sum  from  90,  if  the 
remainder  exceed  23^  degrees,  there  can  be  no  constant  twilight  at  the  given 
place. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


227 


PROBLEM  XXXVII. 

To  find  the  duration  of  twilight  at  the  north  pole. 

Rule.  Elevate  the  north  pole  so  that  the  equator  may  coin- 
cide with  the  horizon  ;  observe  what  point  of  the  ecliptic  nearest 
to  Libra  passes  under  18^  belovs^  the  horizon, reckoned  on  the  brass 
meridian,  and  find  the  day  of  the  month  correspondent  thereto  ; 
the  time  elapsed  from  the  23d  of  September  to  this  time  will  be 
the  duration  of  evening  twilight.  Secondly,  observe  what  point 
of  the  ecliptic,  nearest  to  Aries,  passes  under  18  below  the  hori- 
zon, reckoned  on  the  brass  meridian,  and  find  the  day  of  the 
month  correspondent  thereto ;  the  time  elapsed  from  that  day  to 
the  21st  of  March  will  be  the  duration  of  morning  twilight. 

Examples.  1.  What  is  the  duration  of  twilight  at  the  north 
pole,  and  what  is  the  duration  of  dark  night  there  ? 

Answer.  The  point  of  the  ecliptic  nearest  to  Libra  which  passes  under  18  de- 
grees below  the  horizon,  is  22  degrees  in  fll,  answering  to  the  13th  of  November ; 
hence  the  evening  twilight  continues  from  the  23d  of  September  (the  end  of  the 
longest  day)  to  the  13th  of  November  the  beginning  of  dark  night)  being  51  days. 
The  point  of  the  ecHptic  nearest  to  Aries  which  passes  under  18  degrees  below  the 
horizon  is  9  degrees  in  answering  to  the  29th  of  January  ;  hence  the  morning 
twilight  continues  from  the  29th  of  January  to  the  21st  of  March  (the  beginning 
of  the  longest  day)  being  51  days.  From  the  23d  of  September  to  the  21st  of 
March  are  179  days,  from  which  deduct  102  (=51  X  2),  the  remainder  is  77 
days,  the  duration  of  total  darkness  at  the  north  pole  ;  but,  even  during  this  short 
period,  the  moon  and  the  Aurora  Borealis  shine  with  uncommon  splendour. 


PROBLEM  XXXVIIL 

To  find  in  what  climate  any  given  place  on  the  globe  is  situated. 

Rule.  1.  If  the  place  be  not  in  the  frigid  zone,  find  the  length 
of  the  longest  day  at  that  place  (by  Problem  XXVIII.)  and  sub- 
tract twelve  hours  therefrom;  the  number  of  half  hours  in  the 
remainder  will  show  the  climate. 

2.  If  the  place  be  in  the  frigid  zone,*  find  the  length  of  the 
longest  day  at  that  place  (by  Problem  XXX.),  and  if  that  be  less 
than  thirty  days,  the  place  is  in  the  twenty-fifth  climate,  or  ihe  first 
within  the  polar  circle.  If  more  than  thirty  and  less  than  sixty 
it  is  in  the  twenty-sixth  climate,  or  the  second  within  the  polar 
circle  ;  if  more  than  sixty,  and  less  than  ninety,  it  is  in  the  twenty- 
seventh  climate,  or  the  third  within  the  polar  circle,  &;c. 


*  The  climates  between  the  polar  circles  and  the  poles  were  unknown  to  the 
ancient  geographers ;  they  reckoned  only  seven  climates  north  of  the  equator. 
The  middle  of  the  first  northern  climate  they  made  to  pass  through  Meroe,  a 


228 


PROBLEMS  PERFORMED  BY 


Part  III. 


Examples.  1.  In  what  climate  is  London,  and  what  other 
remarkable  places  are  situated  in  the  same  climate  ? 

^Answer.  The  longest  day  in  London  is  16.^  hours;  if  we  deduct  12  therefrom, 
the  remainder  will  be  4^  hours,  or  nine  half  hours;  hence  London  is  in  the  ninth 
climate  north  of  the  equator ;  and  as  all  places  in  or  near  the  same  latitude  are  in 
the  same  climate,  we  shall  find  Amsterdam,  Dresden,  Warsaw,  Irkoutsk,  the 
southern  part  of  the  peninsula  of  Kamtschatka,  Nootka  Sound,  the  South  of  Hud- 
son's Bay,  the  north  of  Newfoundland,  &c.  to  be  in  the  same  climate  as  London. 
The  learner  is  requested  to  turn  to  the  note  to  Definition  69th,  page  38. 

2.  In  what  climate  is  the  North  Cape  in  the  island  of  Mag- 
geroe,  latitude  71°  30'  north  ? 

Answer.  The  length  of  the  longest  day  is  77  days  ;  these  days  divided  by  30 
give  two  months  for  the  quotient,  and  a  remainder  of  17  days ;  hence  the  place  is  in 
the  third  climate  within  the  polar  circle,  or  the  27th  climate  reckoning  from  the 
equator.  The  southern  part  of  Nova  Zembla,  the  northern  part  of  Siberia,  James* 
Island,  Baffin's  Bay,  the  northern  part  of  Greenland,  &c,  are  in  the  same  climate. 

3.  In  what  climate  is  Edinburgh,  and  what  other  places  are 
situated  in  the  same  climate  ? 

4.  In  what  climate  is  the  north  of  Spitzbergen? 

5.  In  what  climate  is  Cape  Horn? 

6.  In  what  climate  is  Botany  Bay,  and  what  other  places  are 
situated  in  the  same  climate  ? 


PROBLEM  XXXIX. 

To  find  the  breadths  of  the  several  climates  between  the  equator 
and  the  polar  circles. 

Rule.  For  the  northern  climates.  Elevate  the  north  pole  23^° 
above  the  northern  point  of  the  horizon  ;  bring  the  sign  Cancer  to 


city  of  Ethiopia,  built  by  Cambyses  on  an  island  in  the  Nile,  nearly  under  the  tropic 
of  Cancer  ;  the  second  through  Syene,  a  city  of  Thebais,  in  Upper  Egypt,  near  the 
cataracts  of  the  Nile;  the  third  through  Alexandria;  the  fourth  through  Rhodes; 
the  fifth  through  Rome  or  the  Hellespont ;  the  sixth  through  the  mouth  of  the  Bo- 
rysthenes  or  Dnieper;  and  the  seventh  through  the  Riphcean  mountains,  supposed  to 
be  situated  near  the  source  of  the  Tanais  or  Don  river.  The  southern  parts  of  the 
earth  being  in  a  great  measure  unknown,  the  chmates  received  their  names  from 
the  northern  ones,  and  not  from  particular  towns  or  places.  Thus  the  climate, 
which  was  supposed  to  be  at  the  same  distance  from  the  equator  southward  as 
Meroe  was  northward,  was  called  Anti-diameroes,  or  the  opposite  climate  to  Meroe; 
Antidiasyenes  was  the  opposite  climate  to  Syenes,  &c. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


229 


the  meridian,  and  set  the  index  to  twelve ;  turn  the  globe  east- 
ward on  its  axis  till  the  index  has  passed  over  a  quarter  of  an 
hour;  observe  that  particular  point  of  the  meridian  passing 
through  Libra,  which  is  cut  by  the  horizon,  and  at  the  point  of 
intersection  make  a  mark  with  a  pencil ;  continue  the  motion  of 
the  globe  eastward  till  the  index  has  passed  over  another  quarter 
of  an  hour,  and  make  a  second  mark ;  proceed  thus  till  the  me- 
ridian passing  through  Libra^  will  no  longer  cut  the  horizon ;  the 
several  marks  brought  to  the  brass  meridian  will  point  out  the 
latitude  where  each  climate  ends.f 

Examples.  1.  What  is  the  breadth  of  the  ninth  north  climate, 
and  what  places  are  situated  within  it? 

Answer.  The  breadth  of  the  9th  climate  is  2»  57' ;  it  begins  in  latitude  49°  2' 
north,  and  ends  in  latitude  51^  59'  north,  and  all  places  situated  within  this  space 
are  in  the  same  climate.  The  places  will  be  nearly  the  same  as  those  enumerated 
in  the  first  example  to  the  preceding  problem. 

2.  What  is  the  breadth  of  the  second  climate,  and  in  what  lat- 
itude does  it  begin  and  end  1 

3.  Required  the  beginning,  end,  and  breadth  of  the  fifth  cli- 
mate. 

4.  What  is  the  breadth  of  the  seventh  climate  north  of  the 
equator,  in  what  latitude  does  it  begin  and  end,  and  what  places 
are  situated  within  it  ? 

5.  What  is  the  breadth  of  the  climate  in  which  Petersburg  is 
situated  ? 

6.  What  is  the  breadth  of  the  climate  in  which  Mount  Heckla 
is  situated  ? 


PROBLEM  XL. 

To  find  that  part  of  the  equation  of  time  which  depends  on  the 
obliquity  of  the  ecliptic. 

Rule.  Find  the  sun's  place  in  the  ecliptic,  and  bring  it  to  the 
brass  meridian ;  count  the  number  of  degrees  from  Aries  to  the 


*  On  Adams'  and  Gary's  globes,  the  meridian  passing  through  Libra  is  divided 
into  degrees,  in  the  same  manner  as  the  brass  meridian  is  divided ;  the  horizon 
will,  therefore,  cut  this  meridian  in  the  several  degrees  answering  to  the  end  of 
each  climate,  without  the  trouble  of  bringing  it  to  the  brass  meridian,  or  marking 
the  globe. 

t  See  a  Table  of  the  climates,  with  the  method  of  constructing  it,  at  pages  39 
and  40. 


230 


PROBLEMS  PERFORMED  BY 


Part  III. 


brass  meridian,  on  the  equator  and  on  the  ecliptic ;  the  differ- 
ence, reckoning  four  minutes  of  time  to  a  degree,  is  the  equation 
of  time.  If  the  number  of  degrees  on  the  ecliptic  exceed  those 
on  the  equator,  the  sun  is  faster  than  the  clock ;  but  if  the  num- 
ber of  degrees  on  the  equator  exceed  those  on  the  ecliptic,  the 
sun  is  slower  than  the  clock. 


Kote.  The  equation  of  time,  or  difference  between 
the  time  shown  by  a  well  regulated  clock,  and  a  true 
sun-dial,  depends  upon  two  causes,  viz.  the  obliquity  of 
the  ecliptic,  and  the  unequal  motion  of  the  earth  in  its 
orbit.  The  former  of  these  causes  may  be  explained 
by  the  above  Problem.  If  two  suns  were  to  set  off 
at  the  same  time  from  the  point  Aries,  and  move  over 
equal  spaces  in  equal  time,  the  one  on  the  echptic, 
the  other  on  the  equator,  it  is  evident  they  would 
never  come  to  the  meridian  together,  except  at  the 
time  of  the  equinoxes,  and  on  the  longest  and  shortest 
days.  The  annexed  table  shows  how  much  the  sun 
is  faster  or  slower  than  the  clock  ought  to  be,  so  far  as 
the  variation  depends  on  the  obHquity  of  the  ecliptic 
only.  The  signs  of  the  first  and  third  quadrants  of 
the  ecliptic  are  at  the  top  of  the  table,  and  the  degrees 
in  these  signs  on  the  left  hand ;  in  any  of  these  signs 
the  sun  is  faster  than  the  clock.  The  signs  of  the 
second  and  third  quadrants  are  at  the  bottom  of  the 
table,  and  the  degrees  in  these  signs  at  the  right  hand ; 
in  any  of  these  signs  the  sun  is  slower  than  the  clock. 

Thus,  when  the  sun  is  in  20  degrees  of  ^  or  flX,  it 
is  9  minutes  50  seconds  faster  than  the  clock,  and, 
when  the  sun  is  in  IS  degrees  of  ^  or  V3,  it  is  6  min- 
utes 2  seconds  slower  than  the  clock. 


Sun  faster  than  the  clock  in 


2au 
4au 


T 


M 

0  0 
0  20 

0  40 

1  0 
1  19 
1  39 

1  59 

2  18 
2  37 
2  56 


16 
34 
53 
11 
29 
47 
4 
21 
5  38 

5  54 

6  10 
6  26 
6  41 

6  35 

7  9 
7  23 
7  36 

7  49 

8  1 
8  13 
8  24 


a 


M.  S. 

8  46 
8  36 
8  25 
8  14 
8  1 
7  49 
7  35 
7  21 
7  6 


51 
35 
19 

2 
45 
27 

9 
50 
4  31 


2  51 
2  30 
2  9 
1  48 
1  27 
1  5 
0  43 
0  22 
0  0 


V3 


lau 
3au 


Sun  slower  than  the  clock  i 


Chap.  I.  THE  TERRESTRIAL  GLOBE.  231 

Examples.  1.  What  is  the  equation  of  time  on  the  17th  of 
July? 

Answer.  The  degrees  on  the  equator  exceed  the  degrees  on  the  ecliptic  by  two  : 
hence  the  sun  is  eight  minutes  slower  than  the  clock.* 

2.  On  what  four  days  of  the  year  is  the  equation  of  time  noth- 
ing? 

3.  What  is  the  equation  of  time  dependant  on  the  obliquity  of 
the  ecHptic  on  the  27th  of  October  ? 

4.  When  the  sun  is  in  18°  of  Aries,  what  is  the  equation  of 
time  ? 


PROBLEM  XLI. 

To  find  the  sun's  meridian  altitude  at  any  time  of  the  year  at  any 

given  place. 

Rule.  Find  the  sun's  dechnation,  and  elevate  the  pole  to  that 
declination  ;  bring  the  given  place  to  the  brass  meridian,  and 
count  the  number  of  degrees  on  the  brass  meridian  (the  nearest 
way)  to  the  horizon ;  these  degrees  will  show  the  sun's  meridian 
altitude.f 

Note.  Tht  sun's  altitude  may  be  found  at  any  particidar  hour,  in  the  following  manner. 

Find  the  sun's  dechnation,  and  elevate  the  pole  to  that  declination ;  bring  the 
given  place  to  the  brass  meridian  and  set  the  index  to  12 ;  then,  if  the  given  time  be 
before  noon,  turn  the  globe  westward  as  many  hours  as  the  time  wants  of  noon ; 
if  the  time  be  past  noon,  turn  the  globe  eastward  as  many  hours  as  the  time  is  past 
noon.  Keep  the  globe  fixed  in  this  position,  and  screw  the  quadrant  of  altitude  on 
the  brass  meridian  over  the  sun's  dechnation;  bring  the  graduated  edge  of  the 
quadrant  to  coincide  with  the  given  place,  and  the  number  of  degrees  between  that 
place  and  the  horizon  will  show  the  sun's  altitude. 

Or, 

Elevate  the  pole  so  many  degrees  above  the  horizon  as  are 
equal  to  the  latitude  of  the  place  ;  find  the  sun's  place  in  the  eclip- 
tic, and  bring  it  to  that  part  of  the  brass  meridian  which  is  num- 


*  The  learner  will  observe  that  the  equation  of  time  here  determined  is  not  the 
true  equation,  as  noted  on  the  7th  circle  on  the  horizon  of  Bardin's  globes ;  the 
equation  of  time  there  given  cannot  be  determined  by  the  globe,  fciee  the  table  at 
the  end  of  Problem  LXIV. 

t  See  Problem  XXI. 


232 


PROBLEMS  PERFORMED  BY 


Part  III. 


bered  from  the  equator  towards  the  poles  ;  count  the  number  of 
degrees  contained  on  the  brass  meridian  between  the  sun's  place 
and  the  horizon,  and  they  will  show  the  altitude.* 

To  find  the  sun's  altitude  at  any  hour,  see  Problem  XLIV. 

Or,  by  the  analemma. 

Elevate  the  pole  so  many  degrees  above  the  horizon  as  are 
equal  to  the  latitude  of  the  place ;  find  the  day  of  the  month  on 
the  analemma,  and  bring  it  to  that  part  of  the  brass  meridian 
which  is  numbered  from  the  equator  towards  the  poles ;  count  the 
number  of  degrees  contained  on  the  brass  meridian  between  the 
given  day  of  the  month  and  the  horizon,  and  they  will  show  the 
altitude. 

To  find  the  sun's  altitude  at  any  hour,  see  Problem  XLIV. 

Examples.  1.  What  is  the  sun's  meridian  altitude  at  London 
on  the  21  st  of  June  ? 

Answer.    62  degrees. 

2.  What  is  the  sun's  meridian  altitude  at  London  on  the  21st 
of  March? 

3.  What  is  the  sun's  least  meridian  altitude  at  London  ? 

4.  What  is  the  sun's  greatest  meridian  altitude  at  Cape  Horn  ? 

5.  What  is  the  sun's  meridian  altitude  at  Madras  on  the  20th 
of  June  ? 

6.  What  is  the  sun's  meridian  altitude  at  Bencoolen  on  the 
15th  of  January? 

Examples  to  the  note. 

1.  What  is  the  sun's  altitude  at  Madrid  on  the  24th  of  August, 
at  11  o'clock  in  the  morning  ?■!- 


*  See  Problem  XXII. 

t  This  example  is  taken  from  a  prospectus,  announcing  the  publication  of  J^ew 
Globes,  to  be  executed  by  Mr.  Dudley  Adams,  and  called  the  JV ewtonian  GlobeSy 
wherein  the  author  has  treated  the  common  globes  with  uncommon  severity  •  he  has, 
however,  been  rather  unfortunate  in  the  choice  of  his  examples,  which  are  designed 
to  show  "  the  absurdities  and  ridiculous  inconsistencies  of  the  common  globes."  He 
says,  "  By  working  this  problem  on  the  common  globes,  we  find,  with  the  greatest 
astonishment,  that  Madrid,  where  it  is  understood  to  be  eleven  o'clock  in  the 
morning,  is  at  that  time  in  the  dark,  under  the  horizon  ;  and  consequently  we 
hardly  conceive  how  the  inhabitants  can  see  the  sun  to  take  its  altitude,  and  calcu- 
late the  time  to  be  eleven  o'clock." — Ex  una  disce  omnes. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


233 


Answer.  The  sun's  declination  is  11^  degrees  north;  by  elevating  the  north 
pole  11^  degrees  above  the  horizon,  and  turning  the  globe  so  that  Madrid  may  be 
one  hour  westward  of  the  meridian,  the  sun's  altitude  will  be  found  to  be  57^^  de- 
grees. 

2.  What  is  the  sun's  altitude  at  London  at  3  o'clock  in  the 
afternoon  on  the  25th  of  April  ? 

3.  What  is  the  sun's  altitude  at  Ronne  on  the  16th  of  January 
at  10  o'clock  in  the  morning  ? 

4.  Required  the  sun's  altitude  at  Buenos  Ayres  on  the  21st  of 
December  at  two  o'clock  in  the  afternoon. 


PROBLEM  XLII. 

When  it  is  midnight  at  any  place  in  the  temperate  or  torrid  zones, 
to  find  the  sun^s  altitude  at  any  place  {on  the  same  meridian)  in 
the  north  frigid  zone,  where  the  sun  does  not  descend  below  the 
horizon. 

Rule.  Find  the  sun's  declination  for  the  given  day,  and  ele- 
vate the  pole  to  that  declination  ;  bring  the  place  (in  the  frigid 
zone)  to  that  part  of  the  brass  meridian  which  is  numbered  from 
the  north  pole  towards  the  equator,  and  the  number  of  degrees 
between  it  and  the  horizon  will  be  the  sun's  altitude. 

Or, 

Elevate  the  north  pole  so  many  degrees  above  the  horizon  as 
are  equal  to  the  latitucJe  of  the  place  in  the  frigid  zone  ;  bring  the 
sun's  place  in  the  ecliptic  to  the  brass  meridian,  and  set  the  index 
of  the  hour-circle  to  twelve ;  turn  the  globe  on  its  axis  till  the 
index  points  to  the  other  twelve  ;  and  the  number  of  degrees  be- 
tween the  sun's  place  and  the  horizon,  counted  on  the  brass  me- 
ridian towards  that  part  of  the  horizon  marked  north,  will  be  the 
sun's  altitude. 

Examples.  1.  What  is  the  sun's  altitude  at  the  North  Cape 
in  Lapland,  when  it  is  midnight  at  Alexandria  in  Egypt  on  the 
21st  of  June  ? 

Answer.    5  degrees. 

2.  When  it  is  midnight  to  the  inhabitants  of  the  island  of  Sicily 
on  the  22d  of  May,  what  is  the  sun's  altitude  at  the  north  of 
Spitzbergen,  in  latitude  80"  north  ? 

3.  What  is  the  sun's  altitude  at  the  north-east  of  Nova  Zembia, 
when  it  is  midnight  at  Tobolsk,  on  the  15th  of  July  ? 

30 


234 


PROBLEMS  PERFORMED  BY 


Part  III. 


4.  What  is  the  sun's  altitude  at  the  north  of  Baffin's  Bay,  when 
it  is  midnight  at  Buenos  Ayres,  on  the  28th  of  May  ? 


PROBLEM  XLIII. 

To  find  the  suvls  amplitude  at  any  place,  the  day  of  the  month 

being  given. 

Elevate  the  pole  so  many  degrees  above  the  horizon  as  are 
equal  to  the  latitude  of  the  given  place  ;  find  the  sun's  place  in 
the  echptic,  and  bring  it  to  the  eastern  semi-circle  of  the  hori- 
zon ;  the  number  of  degrees  from  the  sun's  place  to  the  east  point 
of  the  horizon  will  be  the  rising  amplitude  ;  bring  the  sun's  place 
to  the  western  semi-circle  of  the  horizon,  and  the  number  of  de- 
grees from  the  sun's  place  to  the  west  point  of  the  horizon  will  be 
the  setting  amplitude. 

Or,  by  the  analemma. 

Elevate  the  pole  so  many  degrees  above  the  horizon  as  are 
equal  to  the  latitude  of  the  place  ;  bring  the  day  of  the  month  on 
the  analemma  to  the  eastern  semi-circle  of  the  horizon ;  the  num- 
ber of  degrees  from  the  day  of  the  month  to  the  east  point  of  the 
horizon  will  be  the  rising  amplitude  :  bring  the  day  of  the  month 
to  the  western  semi-circle  of  the  horizon,  and  the  number  of  de- 
grees from  the  day  of  the  month  to  the  west  point  of  the  horizon 
will  be  the  setting  amplitude. 

Examples.  1.  What  is  the  sun's  amplitude  at  London  on  the 
21st  of  June? 

Answer.    39°  48'  to  the  north  of  the  east,  and  39°  48'  to  the  north  of  the  west. 

2.  On  what  point  of  the  compass  does  the  sun  rise  and  set  at 
London  on  the  17th  of  May  ? 

3.  On  what  point  of  the  compass  does  the  sun  rise  and  set  at 
the  Cape  of  Good  Hope  on  the  21st  of  December? 

4.  On  what  point  of  the  compass  does  the  sun  rise  and  set  on 
the  21st  of  March? 

5.  On  what  point  of  the  compass  does  the  sun  rise  and  set  at 
Washington  on  the  21st  of  October? 

6.  On  what  point  of  the  compass  does  the  sun  rise  and  set  at 
Petersburg  on  the  18th  of  December  ? 

7.  On  December  22d,  1825,  in  latitude  2h  38'  S  .  and  longi- 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


235 


tude  83°  W.,  if  the  sun  set  on  the  S.W.  point  of  the  compass, 
what  is  the  variation  ? 

8.  On  the  15th  of  May,  1825,  if  the  sun  rise  E.  by  N.  in 
latitude  33°  15'  N.  and  longitude  18°  W.,  what  is  the  variation  of 
the  compass? 


PROBLEM  XLIV. 

To  find  the  sun^s  azimuth  and  his  altitude  at  any  place,  the  day  and 
hour  being  given. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place,  and  screw  the  quadrant 
of  altitude  on  the  brass  meridian,  over  that  latitude  ;  find  the  sun's 
place  in  the  ecliptic,  bring  it  to  the  brass  meridian,  and  set  the 
index  of  the  hour-circle  to  twelve ;  then  if  the  given  time  be  before 
noon,  turn  the  globe  eastward*  as  many  hours  as  it  wants  of  noon  ; 
but,  if  the  given  time  be  past  noon,  turn  the  globe  westward  as 
many  hours  as  it  is  past  noon ;  bring  the  graduated  edge  of  the 
quadrant  of  altitude  to  coincide  with  the  sun's  place,  then  the 
number  of  degrees  on  the  horizon,  reckoned  from  the  north  or 
south  point  thereof  to  the  graduated  edge  of  the  quadrant,  will 
show  the  azimuth ;  and  the  number  of  degrees  on  the  quadrant 
counting  from  the  horizon  to  the  sun's  place,  will  be  the  sun's 
altitude. 

Or,  by  the  analemma. 

Elevate  the  pole  so  many  degrees  above  the  horizon  as  are 
equal  to  the  latitude  of  the  place,  and  screw  the  quadrant  of 
altitude  on  the  brass  meridian,  over  that  latitude  ;  bring  the  middle 
of  the  analemma  to  the  brass  meridian,  and  set  the  index  of  the 
hour-circle  to  twelve  ;  then,  if  the  given  time  be  before  noon,  turn 
the  globe  eastward  on  its  axis  as  many  hours  as  it  wants  of  noon ; 
but,  if  the  given  time  be  past  noon,  turn  the  globe  westward  as 


*  Whenever  the  pole  is  elevated  for  the  latitude  of  the  place,  the  proper  motion 
of  the  globe  is  from  east  to  west,  and  the  sun  is  on  the  east  side  of  the  brass  meridian 
in  the  morning,  and  on  the  west  side  in  the  afternoon ;  but  when  the  pole  is 
elevated  for  the  sun's  declination,  the  motion  is  from  west  to  east,  and  the  place 
is  on  the  west  side  of  the  meridian  in  the  morning,  and  on  the  east  side  in  the 
afternoon. 


236 


PROBLEMS  PERFORMED  BY 


Part  III. 


many  hours  as  it  is  past  noon  ;  bring  the  graduated  edge  of  the 
quadrant  of  altitude  to  coincide  with  the  day  of  the  month  on 
the  analemma,  then  the  number  of  degrees  on  the  horizon, 
reckoned  from  the  north  or  south  point  thereof  to  the  graduated 
edge  of  the  quadrant,  will  show  the  azimuth  ;  and  the  number  of 
degrees  on  the  quadrant,  counting  from  the  horizon  to  the  day  of 
the  month,  will  be  the  sun's  altitude. 

Examples.  1.  What  is  the  sun's  altitude,  and  his  azimuth 
from  the  north,  at  London,  on  the  first  of  May,  at  ten  o'clock  in 
the  morning  ? 

Jlnswer.  The  altitude  is  47=',  and  the  azimuth  from  the  north  136°,  or  from  the 
south  44°. 

2.  What  is  the  sun's  altitude  and  azimuth  at  Petersburg  on 
the  13th  of  August,  at  half-past  five  o'clock  in  the  morning  ? 

3.  What  is  the  sun's  azimuth  and  altitude  at  Antigua,  on  the 
21st  of  June,  at  half-past  six  in  the  morning,  and  at  half-past 
ten 

4.  At  Barbadoes,  on  the  21st  of  June,  required  the  sun's  azimuth 
and  altitude  at  8  minutes  past  6,  and  at  |  past  nine  in  the  morning : 
also  at  \  past  2,  and  at  52  minutes  past  5  in  the  afternoon. 

5.  On  the  13th  of  August,  at  half-past  eight  o'clock  in  the 
morning,  at  sea  in  latitude  57°  N.  the  observed  azimuth  of  the  sun 
was  S.  40°  14'  E.,  what  was  the  sun's  altitude,  his  true  azimuth, 
and  the  variation  of  the  compass  ? 

6.  On  the  14th  of  January,  in  latitude  33°  52'  S.,  at  half-past 
three  o'clock  in  the  afternoon,  the  sun's  magnetic  azimuth  was 
observed  to  be  N.  63°  51'  W.,  what  was  the  true  azimuth,  the 
variation  of  the  compass,  and  the  sun's  altitude  ? 


*  At  all  places  in  the  torrid  .zone,  whenever  the  declination  of  the  sun  exceeds 
the  latitude  of  the  place,  and  both  are  of  the  same  name,  the  sun  will  appear  twice 
in  the  forenoon  and  twice  in  the  afternoon,  on  the  same  point  of  the  compass,  and 
will  cause  the  shadow  of  an  azimuth  dial  to  go  back  several  degrees.  In  this 
example,  the  sun's  azimuth  at  the  hours  given  above,  will  be  69°  from  the  north 
towards  the  east ;  and  at  half-past  eight  o'clock,  the  sun  will  appear  to  have  the 
same  azimuth  for  some  time. 


Chap.  1. 


THE  TERRESTRIAL  GLOBE. 


237 


PROBLEM  XLV. 

The  latitude  of  the  place,  day  of  the  month,  and  the  suns  altitude 
being  given,  to  find  the  sun^s  azimuth  and  the  hour  of  the  day* 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place,  and  screws  the  quadrant 
of  altitude  on  the  brass  meridian,  over  that  latitude ;  bring  the 
sun's  place  in  the  ecliptic  to  the  brass  meridian,  and  set  the  index 
of  the  hour  circle  to  twelve ;  turn  the  globe  on  its  axis  till  the 
sun's  place  in  the  ecliptic  coincides  with  the  given  degree  of  alti- 
tude on  the  quadrant ;  the  hours  passed  over  by  the  index  of  the 
hour  circle  will  show  the  time  from  noon,  and  the  azimuth  will 
be  found  on  the  horizon,  as  in  the  preceding  problem. 

Or,  by  the  analemma. 

Elevate  the  pole  to  the  latitude  of  the  place,  and  screw  the 
quadrant  of  altitude  over  that  latitude  ;  bring  the  middle  of  the 
analemma  to  the  brass  meridian,  and  set  the  index  of  the  hour 
circle  to  twelve  ;  move  the  globe  and  quadrant  till  the  day  of  the 
month  coincides  with  the  given  altitude,  the  hours  passed  over  by 
the  index  will  show  the  time  from  noon,  and  the  azimuth  will  be 
found  in  the  horizon  as  before. 

Examples.  1.  At  what  hour  of  the  day  on  the  21st  of  March 
is  the  sun's  altitude  !22|°  at  London,  aad  what  is  his  azimuth  ? 
The  observation  being  made  in  the  afternoon. 

Jtnswer.  The  time  from  noon  will  be  found  to  be  3  hours  30  minutes,  and  the 
azimuth  59°  1'  from  the  south  towards  the  west.  Had  the  observations  been  made 
before  noon,  the  time  from  noon  would  have  been  3  1-2  hours,  viz.  it  would  have 
been  30  minutes  past  eight  in  the  morning,  and  the  azimuth  would  have  been 
59°  1'  from  the  south  towards  the  east.f 


+  This  problem  is  only  a  variation  of  the  preceding ;  for,  by  the  nature  of  spher- 
ical trigonometry,  any  three  of  the  following  quantities,  viz.  the  latitude  of  the 
place,  the  sun^s  declination,  altitude,  azimuth,  or  time  of  the  day,  being  given,  the  rest 
may  be  found,  admitting  of  several  variations.  A  large  collection  of  Astronomical 
problems  may  be  found  in  KeitWs  Trigonometry,  fourth  edition,  page  2S1,  &c. 
These  problems  are  useful  exercises  on  the  globes. 

f  The  learner  will  observe,  that  the  sun  has  the  same  altitude  at  equal  distances 
from  noon  ;  hence  it  is  necessary  to  say  whether  the  observation  be  made  before  or 
after  noon,  otherwise  the  problem  admits  of  two  answers. 


238 


PROBLEMS  PERFORMED  BY 


Part  III. 


2.  At  what  hour  on  the  9th  of  March  is  the  sun's  altitude  25° 
at  London,  and  what  is  his  azimuth?  The  observation  being 
made  in  the  forenoon. 

3.  At  what  hour  on  the  18th  of  May  is  the  sun's  altitude  30°  at 
Lisbon,  and  what  is  the  azimuth  ?  The  observation  being  made 
in  the  afternoon. 

4.  Walking  along  the  side  of  Queen-square  in  London,  on  the 
5th  of  August  in  the  forenoon,  I  observed  the  shadows  of  the  iron 
rails  to  be  exactly  the  same  kngth  as  the  rails  themselves ;  pray 
what  o'clock  was  it,  and  on  what  point  of  the  compass  did  the 
shadows  of  the  rails  fall  ? 

5.  In  latitude  13°  30'  N.,  on  the  21st  of  June,  the  sun  had  the 
same  azimuth  at  two  different  times  in  the  morning ;  and  also  in 
the  afternoon,  viz.  when  his  altitude  was  7°  17'  and  56"  55' : 
required  the  azimuth  and  the  hours  of  the  day.  It  is  likewise 
required  to  find  the  azimuth  when  it  is  the  greatest,  and  the  hour ; 
the  altitude  at  that  time  being  35°  50'. 


PROBLEM  XLVI. 

Given  the  latitude  of  the  place,  and  the  day  of  the  month,  to  find  at 
what  hour  the  sun  is  due  east  or  west. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place,  find  the  sun's  place  in  the 
ecliptic,  bring  it  to  the  brass  meridian,  and  set  the  index  of  the 
hour-circle  to  twelve  ;  screw  the  quadrant  of  altitude  on  the  brass 
meridian,  over  the  given  latitude,  and  move  the  lower  end  of  it  to 
the  east  point  of  the  horizon ;  hold  the  quadrant  in  this  position, 
and  move  the  globe  on  its  axis,  till  the  sun's  place  comes  to  the 
graduated  edge  of  the  quadrant ;  the  hours  passed  over  by  the  in- 
dex from  twelve  will  be  the  time  from  noon  when  the  sun  is  due 
east,*  and  at  the  same  time  from  noon  he  will  be  due  west. 


*  If  the  latitude  be  north,  and  the  sun's  declination  be  south,  he  will  be  due  east 
and  west  when  he  is  below  the  horizon ;  and  the  same  thing  will  happen  if  the  lati- 
tude be  south  when  the  dedination  is  north.  Examples  exercising  these  cases  are 
useless ;  however  they  are  easily  solved,  if  we  consider  that,  when  the  sun  is  due 
east  below  the  horizon  at  any  time,  the  opposite  point  of  the  ecliptic  will  be  due 
west  above  the  horizon  :  therefore,  instead  of  bringing  the  lower  edge  of  the  quad- 
rant to  the  east  of  the  horizon,  bring  it  to  the  west,  and,  instead  of  using  the  sun's 
place,  make  use  of  a  point  in  the  ecliptic  diametrically  opposite. 


Chap,  I. 


THE  TERRESTRIAL  GLOBE. 


239 


Or,  by  the  analemma. 

This  is  exactly  the  same  as  above,  only,  instead  of  bringing  the 
sun's  place  to  the  meridian,  you  bring  the  analemma  there,  and, 
instead  of  bringing  the  sun's  place  to  the  graduated  edge  of  the 
quadrant,  the  day  of  the  month  on  the  analemma  must  be  brought 
to  it. 

Examples.  1.  At  what  hour  will  the  sun  be  due  east  at  Lon- 
don on  the  19th  of  May  ;  at  what  hour  will  he  be  due  west ;  and 
what  will  his  altitude  be  at  these  times  ? 

Answer.  The  time  from  12,  when  the  sun  is  due  east,  is  4  hours  54  minutes; 
hence  the  sun  is  due  east  at  six  minutes  past  seven  o'clock,  in  the  morning,  and  due 
west  at  54  minutes  past  four  in  the  afternoon  ;  the  sun's  altitude  will  be  found  at 
the  same  time,  as  in  Problem  XLIV.    In  this  example  it  is  25^  26'. 

2.  At  what  hours  will  the  sun  be  due  east  and  west  at  London 
on  the  21st  of  June,  and  on  the  21st  of  December  ;  and  what  will 
be  his  altitude  above  the  horizon  on  the  21st  of  June? 

3.  Find  at  what  hours  the  sun  will  be  due  east  and  west,  not 
only  at  London  but  at  every  place  on  the  surface  of  the  globe,  on 
the  21st  of  March  and  on  the  23d  of  September. 

4.  At  what  hours  is  the  sun  due  east  and  west  at  Buenos 
Ayres  on  the  21st  of  December? 


PROBLEM  XLVII. 

Given  the  suvls  meridian  altitude^  and  the  day  of  the  month,  to  find 
the  latitude  of  the  place. 

Rule.  Find  the  sun's  place  in  the  ecliptic,  and  bring  it  to  that 
part  of  the  brass  meridian  which  is  numbered  from  the  equator 
towards  the  poles ;  then,  if  the  sun  was  south*  of  the  observer  when 
the  altitude  was  taken,  count  the  number  of  degrees  from  the  sun*s 
place  on  the  brass  meridian  towards  the  south  point  of  the  horizon, 
and  mark  where  the  reckoning  ends  ;  bring  this  mark  to  coincide 
with  the  south  point  of  the  horizon,  and  the  elevation  of  the  north 
pole  will  show  the  latitude.  If  the  sun  was  north  of  the  observer 
when  the  altitude  was  taken,  the  degrees  must  be  counted  in  a 
similar  manner,  from  the  sun's  place  towards  the  north  point  of 


*  It  is  necessary  to  state  whether  the  sun  be  to  the  north  or  south^f  the  ob- 
server at  noon,  otherwise  the  problem  is  unlimited. 


240 


PROBLEMS  PERFORMED  BY 


Part  III. 


the  horizon,  and  the  elevation  of  the  south  pole  will  show  the 
latitude. 

Or,  without  a  globe. 

Subtract  the  sun^s  altitude  from  ninety  degrees,  the  remainder 
is  the  zenith  distance.  If  the  sun  be  south  when  the  altitude  is 
taken,  call  the  zenith  distance  north  ;  but,  if  north,  call  it  south  ; 
find  the  sun's  declination  in  an  ephemeris*  or  a  table  of  the  sun's 
declination,  and  mark  whether  it  be  north  or  south ;  then,  if  the 
zenith  distance  and  declination  have  the  same  name,  their  sum  is 
the  latitude,  but,  if  they  have  contrary  names,  their  difference  is 
the  latitude,  and  it  is  always  of  the  same  name  with  the  greater 
of  the  two  quantities. 

Examples.  1.  On  the  10th  of  May,  1825, 1  observed  the  sun's 
meridian  altitude  to  be  50°,  and  it  was  south  of  me  at  that  time  ; 
required  the  latitude  of  the  place. 

Answer.    57°  37'  north. 

By  calculation. 

90^  0' 

50     OS.,  sun's  altitude  at  noon. 

40     0  N.,  the  zenith's  distance. 

17    37  N.,  the  sun's  declination  10th  May,  1825. 

-     67    37  N.,  the  latitude  sought. 

2.  On  the  10th  of  May,  1825,  the  sun's  meridian  altitude  was 
observed  to  be  50°,  and  it  was  north  of  the  observer  at  that  time  ; 
required  the  latitude  of  the  place. 

»Bnswer.    22' 23' south. 

By  calculation. 

90°  0' 

50     0  N.,  sun's  altitude  at  noon. 

40     0  S.,  the  zenith's  distance. 

17    37  N.,  the  sun's  decUnation  10th  of  May,  1825. 

22    23  S.,  the  latitude  sought. 

3.  On  the  5th  of  August  1825,  the  sun's  meridian  altitude  was 
observed  to  be  74*'  30'  north  of  the  observer  ;  what  was  the  lat- 
itude ? 


*  The  most  convenient  is  the  Nautical  Almanac,  or  White's  Ephemeris ;  see  the 
note  page  57. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


241 


4.  On  the  19th  of  November,  1825,  the  sun's  meridian  altitude 
was  observed  to  be  40°  south  of  the  observer  ;  vs^hat  w^as  the 
latitude  ? 

5.  At  a  certain  place,  vs^here  the  clocks  are  two  hours  faster 
than  at  London,  the  sun's  meridian  altitude  was  observed  to  be 
30  degrees  to  the  south  of  the  observer  on  the  21st  of  March  ; 
required  the  place. 

6.  At  a  place  where  the  clocks  are  five  hours  slower  than  at 
London,  the  sun's  meridian  altitude  was  observed  to  be  60°  to 
the  south  of  the  observer  on  the  16th  of  April,  1825  ;  required 
the  place. 

PROBLEM  XLVlll. 

The  length  of  the  longest  day  at  any  place,  not  within  the  polar 
circles,  being  given,  to  find  the  latitude  of  that  place. 

Rule.  Bring  the  first  point  of  Cancer  or  Capricorn  to  the  brass 
meridian  (according  as  the  place  is  on  the  north  or  south  side  of 
the  equator),  and  set  the  index  of  the  hour  circle  to  twelve  ;  turn 
the  globe  westward  on  its  axis  till  the  index  of  the  hour  circle  has 
passed  over  as  many  hours  as  are  equal  to  half  the  length  of  the 
day  ;  elevate  or  depress  the  pole  till  the  sun's  place  (viz.  Cancer 
or  Capricorn)  comes  to  the  horizon  ;  then  the  elevation  of  the 
pole  will  show  the  latitude. 

Note.  This  problem  will  answer  for  any  day  in  the  year,  as  well  as  the  longest 
day,  by  bringing  the  sun's  place  to  the  brass  meridian  and  proceeding  as  above. 

Or,  bring  the  middle  of  the  analemma  to  the  brass  meridian,  and  set  the  index 
of  the  hour  circle  to  12 ;  turn  the  globe  westward  on  its  axis  till  the  index  has 
passed  over  as  many  hours  as  are  equal  to  half  the  length  of  the  day ;  elevate  or 
depress  the  pole  till  the  day  of  the  month  coincides  with  the  horizon,  then  the 
elevation  of  the  pole  will  show  the  latitude. 

Examples.  1.  In  what  degree  of  north  latitude,  and  at  what 
places  is  the  length  of  the  longest  day  16^  hours  ? 

Answer.  In  latitude  52  ',  and  all  places  situated  on,  or  near  that  parallel  of 
latitude,  have  the  same  length  of  day. 

2.  In  what  degree  of  south  latitude,  and  at  what  places  is  the 
longest  day  14  hours  ? 

3.  In  what  degree  of  north  latitude  is  the  length  of  the  longest 
day  three  times  the  length  of  the  shortest  night  ? 

4.  There  is  a  town  in  Norway  where  the  longest  day  is  five 
times  the  length  of  the  shortest  night ;  pray  what  is  the  name  of 
the  town  ? 

31 


242  PROBLEMS  PERFORMED  BY  Part  III. 

5.  In  what  latitude  north  does  the  sun  set  at  seven  o'clock  on 
the  5th  of  April  ? 

6.  In  what  latitude  south  does  the  sun  rise  at  five  o'clock  on 
the  25th  of  November  ? 

7.  In  what  latitude  north  is  the  20th  of  May  16  hours  long  ? 

8.  In  what  latitude  north  is  the  night  of  the  15th  of  August  10 
hours  long  ? 

PROBLEM  XLIX. 

The  latitude  of  a  place  and  the  day  of  the  month  being  given,  to 
find  how  much  the  sun^s  declination  must  vary  to  make  the  day 
an  hour  longer  or  shorter  than  the  given  daij. 

Rule.  Find  the  sun's  declination  for  the  given  day,  and  elevate 
the  pole  to  that  declination  ;  bring  the  given  place  to  the  brass 
meredian,  and  set  the  index  of  the  hour  circle  to  twelve;  turn 
the  globe  eastward  on  its  axis  till  the  given  place  comes  to  the 
horizon,  and  observe  the  hours  passed  over  by  the  index.  Then, 
if  the  days  be  increasing,  continue  the  motion  of  the  globe  east- 
ward till  the  index  has  passed  over  an  other  half-hour,  and  raise 
or  depress  the  pole  till  the  place  comes  again  into  the  horizon,  the 
elevation  of  the  pole  will  show  the  sun's  declination  when  the  day 
is  an  hour  longer  than  the  given  day  ;  but,  if  the  days  be  decreas- 
ing, after  the  place  is  brought  to  the  eastern  part  of  the  horizon, 
turn  the  globe  westward  till  the  index  has  passed  over  half-an- 
hour,  then  raise  or  depress  the  pole  till  the  place  comes  a  second 
time  into  the  horizon,  the  last  elevation  of  the  pole  will  show  the 
sun's  declination  when  the  day  is  an  hour  shorter  than  the  given 
day. 

Or, 

Elevate  the  pole  to  the  latitude  of  the  place,  find  the  sun's  place 
in  the  ecliptic,  bring  it  to  the  brass  meridian,  and  set  the  index  of 
the  hour  circle  to  twelve  :  turn  the  globe  westward  on  its  axis  till 
the  sun's  place  comes  to  the  horizon,  and  observe  the  hours  passed 
over  by  the  index ;  then,  if  the  days  be  increasing,  continue  the 
n)otion  of  the  globe  westward  till  the  index  has  passed  over  an 
other  half-hour,  and  observe  what  point  of  the  ecliptic  is  cut  by 
the  horizon  ;  that  point  will  show  the  sun's  place  when  the  day 
is  an  hour  longer  than  the  given  day,  whence  the  declination 
is  readily  found;  but,  if  the  days  be  decreasing,  turn  the  globe 
eastward  till  the  index  has  passed  over  half-an-hour,  and  observe 


Chajj.  I. 


THE  TERRESTRIAL  GLOBE. 


243 


what  point  of  the  ecliptic  is  cut  by  the  horizon;  that  point 
will  show  the  sun's  place  when  the  day  is  an  hour  shorter  than 
the  given  day. 

Or,  by  THE  ANALEMMA. 

Proceed  exactly  the  same  as  above,  only,  instead  of  bring- 
ing the  sun's  place  to  the  brass  meridian,  bring  the  analemma 
there,  and  instead  of  the  sun's  place,  use  the  day  of  the  month 
on  the  analemma. 

Examples.  1.  How  much  must  the  sun's  declination  vary 
that  the  day  at  London  may  be  increased  one  hour  from  the 
24th  of  February? 

Answer.  On  the  24th  of  February  the  sun's  declination  is  9°  38'  south,  and  the 
sun  sets  at  a  quarter  past  five  j  when  the  sun  sets  at  three  quarters  past  five,  his 
dedination  will  be  found  to  be  about  4|  south  answering  to  the  tenth  of  March  : 
hence  the  dechnation  has  decreased  5  >  23',  and  the  days  have  increased  1  hour  in 
14  days. 

2.  How  much  must  the  sun's  declination  vary  that  the  day  at 
London  may  decrease  one  hour  in  length  from  the  26th  of  July  ? 

Answer,  The  sun's  declination  on  the  26th  of  July  is  19°  38'  north,  and  the  sun 
sets  at  49  min.  past  seven  ;  when  the  sun  sets  at  19  minutes  past  seven,  his  decli- 
nation will  be  found  to  be  14  43'  north,  answering  to  the  13th  of  August :  hence 
the  declination  has  decreased  5^  55',  and  the  days  have  decreased  one  hour  in  18 
days. 

3.  How  much  must  the  sun's  declination  vary  from  the  5th 
of  April,  that  the  day  at  Petersburg  may  increase  one  hour? 

4.  How  much  mwsi  the  sun's  declination  vary,  from  the  4th  of 
October,  that  the  day  at  Stockholm  may  decrease  one  hour  ? 

5.  What  is  the  difference  in  the  sun's  declination,  when  he  rises 
at  seven  o'clock  at  Petersburg,  and  when  he  sets  at  nine  ? 


PROBLEM  L. 

To  find  the  sun^s  right  ascension^  oblique  ascension,  oblique 
descension,  ascensional  difference,  and  time  of  rising  and  setting 
at  any  given  place,  the  day  of  the  month  being  given. 

Rule.  Find  the  sun's  place  in  the  ecliptic,  and  bring  it  to 
that  part  of  the  brass  meridian  which  is  numbered  from  the  equa- 
tor towards  the  poles     the  degree  on  the  equator  cut  by  the 


*  The  degree  on  the  meridian  above  the  sun's  place  is  the  sun's  declination. 
See  Problem  XX. 


244 


PROBLEMS  PERFORMED  BY 


Part  III. 


graduated  edge  of  the  brass  meridian,  reckoning  from  the  point 
Aries  eastward,  will  be  the  sun's  right  ascension. 

Elevate  the  poles  so  many  degrees  above  the  horizon  as  are 
equal  to  the  latitude  of  the  place,  bring  the  sun's  place  in  the 
ecliptic  to  the  eastern  part  of  the  horizon,*  and  the  degree  on 
the  equator  cut  by  the  horizon,  reckoning  from  the  point  Aries 
eastward,  will  be  the  sun's  oblique  ascension.  Bring  the  sun's 
place  in  the  ecliptic  to  the  western  part  of  the  horizon,f  and  the 
degree  on  the  equator  cut  by  the  horizon,  reckoning  from  the 
point  Aries  eastward,  will  be  the  sun's  oblique  descension. 

Find  the  difference  between  the  sun's  right  and  oblique  ascen- 
sion, or,  which  is  the  same  thing,  the  difference  between  the 
right  ascension  and  oblique  descension,  and  turn  this  difference 
into  time  by  multiplying  by  four,J  then,  if  the  sun's  declination 
and  the  latitude  of  the  place  be  both  of  the  same  name,  viz.  both 
north  or  both  south,  the  sun  rises  before  six  and  sets  after  six,  by 
a  space  of  time  equal  to  the  ascensional  difference ;  but  if  the 
sun's  declination  and  the  latitude  be  of  contrary  names,  viz.  the 
one  north  and  the  other  south,  the  sun  rises  after  six  and  sets  be- 
fore six. 

Examples.  1.  Required  the  sun's  right  ascension,  oblique  as- 
cension, oblique  descension,  ascensional  difference,  and  time  of 
rising  and  setting  at  London,  on  the  15th  of  April  ? 

Answer.  The  right  ascension  is  SS'^  30',  the  oblique  ascension  is  9°  45',  the  as- 
censional difference  (23^  30' —  9;  45'  =)  13°  45',  or  55  nniinutes  of  time  ;  conse- 
quently the  sun  rises  55  minutes  before  six,  or  5  minutes  past  5,  and  sets  55  min- 
utes past  6.  The  oblique  descension  is  37°  15';  consequently  the  descensional 
difference  is  (37^  15' — 23°  30'=)  13°  45'  the  same  as  the  ascensional  difference. 

2.  What  are  the  sun's  right  ascension,  oblique  ascension,  and 
oblique  descension,  on  the  27th  of  October  at  London ;  what  is 
the  ascensional  difference,  and  at  what  time  does  the  sun  rise 
and  set  ? 

3.  What  are  the  sun's  right  ascension,  declination,  oblique  as- 
cension, rising  amplitude,  oblique  descensibn,  and  setting  ampli- 
tude at  London,  on  the  1st  of  May  ;  what  is  the  ascensional  dif- 
ference, and  at  what  time  does  the  sun  rise  and  set  ? 

4.  What  are  the  sun's  right  ascension,  declination,  oblique  as- 
cension, rising  amplitude,  oblique  descension,  and  setting  ampli- 


*  The  rising  amplitude  may  be  seen  at  the  same  time.    See  Problem  XLIII. 
t  The  setting  ampUtude  may  here  be  seen.    Vide  Problem  XLIII. 
X  See  Problem  XVIII. 


Chap,  I. 


THE  TERRESTRIAL  GLOBE. 


tude  at  Petersburg,  on  the  21st  of  June  ;  what  is  the  ascensional 
difference,  and  at  what  time  does  the  sun  rise  and  set  ? 

5.  What  are  the  sun's  right  ascension,  decHnation,  oblique  as- 
cension, rising  amplitude,  oblique  descension,  and  setting  ampli- 
tude, at  Alexandria,  on  the  21st  of  December :  what  is  the  ascen- 
sional difference,  and  at  what  time  does  the  sun  rise  and  set  ? 


PROBLEM  LI. 

Given  the  day  of  the  month  and  the  sun^s  amplitude,  to  find  the 
latitude  of  the  place  of  observation. 

Rule.  Find  the  sun's  place  in  the  echptic,  and  bring  it  to  the 
eastern  or  western  part  of  the  horizon  (according  as  the  eastern 
or  western  amplitude  is  given)  ;  elevate  or  depress  the  pole  till 
the  sun's  place  coincides  with  the  given  amplitude  on  the  horizon, 
then  the  elevation  of  the  pole  will  show  the  latitude. 

Or,  thus  : 

Elevate  the  north  pole  to  the  complement*  of  the  amplitude, 
and  screw  the  quadrant  of  altitude  upon  the  brass  meridian  over 
the  same  degree :  bring  the  equinoctial  point  Aries  to  the  brass 
meridian,  and  move  the  quadrant  of  altitude  till  the  sun's  declina- 
tion for  the  given  day  (counted  on  the  quadrant)  coincides  with 
the  equator;  the  number  of  degrees  between  the  point  Aries 
and  the  graduated  edge  of  the  quadrant  will  be  the  latitude 
sought. 

Examples.  1.  The  sun's  amplitude  was  observed  to  be  39°  48'  • 
from  the  east  towards  the  north,  on  the  21st  of  June ;  required 
the  latitude  of  the  place  ? 

Ansvjer.    51°  32'  north.f 

2.  The  sun's  amplitude  was  observed  to  be  15"  30'  from  the 


*  The  complement  of  the  amplitude  is  found  by  subtracting  the  amplitude  from 
Q0°.  This  rule  is  exactly  the  same  as  above ;  for  it  is  formed  from  a  right-angled 
spherical  triangle,  the  base  being  the  complement  of  the  amplitude,  the  perpendic- 
ular the  latitude  of  the  place,  and  the  hypothenuse  the  complement  of  the  sun's 
declination. 

t  See  Keith^s  Trigonometry,  fourth  edition,  page  285. 


346 


PROBLEMS  PERFORMED  BY 


Part  III. 


east  towards  the  north,  at  the  same  time  his  decHcation  was  15° 
30' ;  required  the  latitude. 

3.  On  the  29th  of  may,  when  the  sun's  declination  was  31°  30' 
north,  his  rising  amplitude  was  known  to  be  22°  northward  of  the 
east  ?  required  the  latitude. 

4.  When  the  sun's  declination  was  2°  north,  his  rising  ampli- 
tude was  4°  north  of  the  east ;  required  the  latitude. 


PROBLEM  LII. 

Given  two  observed  altitudes  of  the  sun,  the  time  elapsed  between 
thenif  and  the  sun^s  declination,  to  find  the  latitude. 

Rule.  Find  the  sun's  declination,  either  by  the  globe  or  an 
ephemeris ;  take  the  number  of  degrees  contained  therein  from 
the  equator  with  a  pair  of  compasses,  and  apply  the  same  num- 
ber of  degrees  upon  the  meridian  passing  through  Libra*  from 
the  equator  northward  or  southward,  and  mark  where  they  ex- 
tend to ;  turn  the  elapsed  time  into  degrees,t  and  count  those  de- 
grees upon  the  equator  from  the  meridian  passing  through  Libra ; 
bring  that  point  of  the  equator  where  the  reckoning  ends  to  the 
graduated  edge  of  the  brass  meridian,  and  set  off  the  sun's  decli- 
nation from  that  point  along  the  edge  of  the  meridian,  the  same 
way  as  before  ;  then  take  the  complement  of  the  first  altitude 
from  the  equator  in  your  compasses,  and,  with  one  foot  in  the 
sun's  decHnation,  and  a  fine  pencil  in  the  other  foot,  describe  an 
arc ;  take  the  complement  of  the  second  altitude  in  a  similar  man- 
ner from  the  equator,  and  with  one  foot  of  the  compasses  fixed 
in  the  second  point  of  the  sun's  declination,  cross  the  former  arc  ; 
the  point  of  intersection  brought  to  that  part  of  the  brass  meridian 
which  is  numbered  from  the  equator  towards  the  poles,  will  stand 
under  the  degree  of  latitude  sought.  J 


*  Any  meridian  will  answer  the  purpose  as  well  as  that  which  passes  through 
Libra ;  on  Adam's  and  on  Gary's  globes  this  meridian  is  divided  like  the  brass 
meridian. 

t  See  the  method  of  turning  time  into  degrees.    Prob.  XIX. 

X  The  calculation  of  this  problem  by  spherical  trigonometry,  and  also  the  ana- 
lytical calculation  are  given  in  Emerson's  Algebra,  pages  446,  and  447,  second 
edition.  In  applying  the  problem  to  Nautical  Astromomy  it  is  usual  to  give  also 
the  latitude  by  account,  from  which  the  true  latitude  is  obtained  by  corrective  ap- 
proximation. 


Chap.  I. 


THE   TERRESTRIAL  GLOBE. 


247 


Examples.  1.  Suppose  on  the  4th  of  June  1825,  in  north 
latitude,  the  sun's  altitude  at  29  minutes  past  10  in  the  forenoon, 
to  be  65°  24',  and  31  minutes  past  12,  74°  8' :  required  the  latitude. 

Ansxoer.  The  sun's  declination  is  22"  26'  north,  the  elapsed  time  two  hours  two 
minutes,  answering  to  30  30' ;  the  complement  of  the  first  altitude  24®  36',  the 
complement  of  the  second  altitude  15"  52',  and  the  latitude  sought  36°  57'  north. 

2.  ^  Given  the  sun's  declination  19°  39'  north,  his  altitude  in 
the  forenoon  38°  19',  and,  at  the  end  of  one  hour  and  a  half,  the 
same  morning,  the  altitude  was  50°  25' ;  required  the  latitude  of 
the  place,  supposing  it  to  be  north. 

3.  When  the  sun's  declination  was  22°  40'  north,  his  altitude  at 
lOh.  54m.  in  the  forenoon  was  53°  29',  and  Ih.  17m.  in  the  af- 
ternoon it  was  52°  48' ;  required  the  latitude  of  the  place  of  ob- 
servation, supposing  it  to  be  north. 

4.  In  north  latitude,  when  the  sun's  declination  was  22°  23' 
south,  the  sun's  altitude  in  the  afternoon  was  observed  to  be  14° 
46',  and  after  Ih.  22m.  had  elapsed,  his  altitude  was  8°  27';  re- 
quired the  latitude. 


PROBLEM  LIII. 


The  day  and  hour  being  given  when  a  solar  eclipse  will  happen^ 
to  find  where  it  will  he  visible. 

Rule.  Find  the  sun's  declination,  and  elevate  the  pole  agree- 
ably to  that  declination  ;  bring  the  place  at  which  the  hour  is 
given  to  that  part  of  the  brass  meridian  which  is  numbered  from 
the  equator  towards  the  poles,  and  set  the  index  of  the  hour  circle 
to  twelve  ;  then,  if  the  given  time  be  before  noon,  turn  the  globe 
westward  till  the  index  has  passed  over  as  many  hours  as  the 
given  time  wants  of  noon  ;  if  the  time  be  past  noon,  turn  the  globe 
eastward  as  many  hours  as  it  is  past  noon,  and  exactly  under  the 


*  A  great  variety  of  examples  accurately  calculated  by  a  general  rule,  without 
an  assumed  latitude,  may  be  seen  in  KeiWs  Trigonometry,  fourth  edition  page 
323,  &c. 


248 


PROBLEMS  PERJ^ORMED  BY 


Part  III. 


degree  of  the  sun's  decimation  on  the  brass  meridian  you  will  find 
the  place  on  the  globe  where  the  sun  will  be  vertically  eclipsed* : 
at  all  places  within  70  degrees  of  this  place,  the  eclipse  may\  be 
visible,  especially  if  it  be  a  total  eclipse. 

Example.  On  the  11th  of  February,  1804,  at  27  min.  past  ten 
o'clock  in  the  morning  at  London,  there  was  an  eclipse  of  the  sun : 
where  was  it  visible,  supposing  the  moon's  penumbra!  shadow  to 
extend  northward  70  degrees  from  the  place  where  the  sun  was 
vertically  eclipsed  ? 

Answer.  London,  &c.  For  more  examples  consult  the  Table  of  Eclipses,  fol- 
lowing the  next  problem. 


l^ROBLEM  LIV. 

The  day  and  hour  being-  given  when  a  lunar  eclipse  will  happen, 
to  find  where  it  will  be  visible. 

Rule.  Find  the  sun's  declination  for  the  given  day,  and  note 
whether  it  be  north  or  south  ;  if  it  be  north,  elevate  the  south 
pole  so  many  degrees  above  the  horizon  as  are  equal  to  the  de- 
clination ;  if  it  be  south,  elevate  the  north  pole  in  a  similar  man- 
ner ;  bring  the  place  at  which  the  hour  is  given  to  that  part  of  the 
brass  meridian  which  is  numbered  from  the  equator  towards  the 
poles,  and  set  the  index  of  the  hour  circle  to  twelve ;  then,  if  the 
given  time  be  before  noon,  turn  the  globe  westward  as  many 
hours  as  it  wants  of  noon  ;  if  after  noon,  turn  the  globe  eastward 
as  many  hours  as  it  is  past  noon ;  the  place  exactly  under  the 
degree  of  the  sun's  declination  will  be  the  antipodes  of  the  place 
where  the  moon  is  vertically  eclipsed,  set  the  index  of  the  hour 
circle  again  to  twelve,  and  turn  the  globe  on  its  axis  till  the  index 
has  passed  over  twelve  hours :  then  to  all  places  above  the  hori- 
zon the  eclipse  will  be  visible  ;  to  those  places  along  the  western 
edge  of  the  horizon,  the  moon  will  rise  eclipsed ;  to  those  along 
the  eastern  edge  she  will  set  eclipsed ;  and  to  that  place  immedi- 


*  The  effect  of  parallax  is  so  great,  that  an  eclipse  may  not  be  visible  even  where 
the  sun  is  vertical. 

I  When  the  moon  is  exactly  in  the  node,  and  when  the  axes  of  the  moon's 
shadow  and  penumbra  pass  through  the  centre  of  the  earth,  the  breadth  of  the 
earth's  surface  under  the  penumbral  shadow  is  70°  20';  but  the  breadth  of  this 
shadow  is  variable  ;  and  if  it  be  not  accurately  determined  by  calculation,  it  is  im- 
possible to  tell  by  the  globe  to  what  extent  an  eclipse  of  the  sun  will  be  visible. 


Chap.  L 


THE  TERRESTRIAL  GLOBE. 


249 


ately  under  the  degree  of  the  sun's  declination,  reckoned  towards 
the  elevated  pole,  the  moon  will  be  vertically  eclipsed. 

Example.  On  the  26th  of  January  1804,  at  58  rnin.  past  seven 
in  the  afternoon  at  London,  there  was  an  eclipse  of  the  moon  ; 
where  was  it  visible  ? 

Answer.  It  was  visible  to  the  whole  of  Europe,  Africa,  and  the  continent  of 
Asia.    For  more  examples  see  the  following  Table  of  Eclipses. 

JN'oTE.  The  substance  of  the  following  Table  of  Eclipses  was  extracted  from 
Dr.  Huttori's  translation  of  Montucla's  edition  of"  Ozanani's  Mathematical  and  Physical 
Recreations,  published  by  Mr.  Kearsley  in  Fleet-street.  These  eclipses  were 
originally  calculated  by  M.  Pingre,  a  member  of  the  Academy  of  Sciences,  and 
published  in  U  Jlrt  de  verifier  les  Dates.  In  classing  these  tables  the  arrangement 
of  Mr.  Ferguson  has  been  followed  ;  see  page  267  of  his  Astronomy,  where  a  cat- 
alogue of  the  visible  eclipses  is  given  from  1700  to  1800,  taken  from  L'  .^rt  de  veri- 
fier les  Dates.  It  may  be  necessary  to  inform  the  learner,  that  the  times  of  these 
eclipses,  as  calculated  by  M.  Pingre,  are  not  perfectly  accurate,  and  were  only  de- 
signed to  show  nearly  the  time  v/hen  an  eclipse  may  be  expected  to  happen.  The 
limits  where  these  eclipses  are  visible  are  generally  from  the  tropic  of  Cancer  in 
Africa,  to  the  northern  extremity  of  Lapland,  and  from  the  5th  degree  of  north  lat- 
itude in  Asia,  to  the  north  polar  circle  ;  though  some  few  of  them  are  visible  be- 
yond the  pole.  In  longitude,  the  limits  are  the  fifth  and  155th  meridians,  supposing 
the  20th  to  pass  through  Paris ;  hence  it  appears  that  they  are  calculated  for  the 
meridian  of  Ferro;  which  will  make  their  limits  from  London  to  be  from  12  '  46' 
west  long,  to  137°  14'  east.  M.  Pingre  says,  that  an  eclipse  of  the  sun  is  visible 
from  32°  to  64°  north,  and  as  far  south  of  the  place  where  it  is  central.  In  the  fol- 
lowing table  the  moon  is  represented  by  §),  the  sun  by  T  stands  for  total,  P  for 
partial,  M  for  morning,  and  A  for  afternoon,  the  rest  is  obvious. 


32 


250  PROBLEMS  PERFORMED  BY  Part  III 


Months 
and 
Days. 


1826 


1827 


1828 


1829 


1830 


1831 


1832 
1833 


1834 
1835 

1836 

1837 

1838 
1839 
1840 

1841 

1842 

1843 

1844 
1845 


Time. 


i)  T 
©  T 

m 
m 

i)  p 
i)  p 

# 


m  p 
f)  p 
m 
m 
m  T 
m  T 
m  p 
m  p 
m 
m  p 
m  p 
m 

€)  T 

m  T 
i)  p 

i)  p 
m 
m  T 

i)  p 

i)  T 

i) 


T 

i)  p 
i)  p 

m 
m 

§)  p 
i)  p 

i)  T 

m 

e  T 

€>  P 

m 

e  p 
<D  p 
i)  p 

i)  T 
i)  T 

i)  T 


May  21 
Nov.  14 
Nov.  29 
April  26 
May  11 
Nov.  3 
April  14 
Oct.  9 
March  20 
Sept.  13 
Sept.  28 
Feb.  23 
March  9 
Sept.  2 
Feb.  26 
Aug.  23 
.July  27 
Jan.  6 
July  2 
July  17 
Dec.  26 
June  21 
Dec.  16 
May  27 
June  10 
Nov.  20 
May  1 
May  15 
Oct.  24 
April  20 
May  4 
Oct.  13 
April  10 
Oct.  3 
MarchlS 
Sept.  7 
Feb.  17 
March  4 
Aug.  13 
Feb.  6 
Feb.  21 
July  18 
Aug.  2 
Jan.  26 
July  8 
July  22 
June  12 
Dec.  7 
Dec.  21 
May  31 
Nov.  25 
May  6 
May  21 


4h  A 
111  M 
H  M 
8|M 
5  A 
9|M 

01  M 

2  A 

7  M 
2iM 
5  M 

2  A 
11  A 

5  A 
lOJM 
2|  A 

8  M 

1  M 
7  M 

10  A 
8iM 
5|M 
U  A 

11  A 
11  M 

8iM 
H  A 
1|  A 

9  A 
U  A 

ll|  A 
2AM 

3  A 
2i  A 

10^  A 

2  A 

4  M 
7iM 
2iM 

11  M 


A 
M 
A 
M 
M 
M 


5^M 
11  A 

0|M 
ICiM 

4k  A 


1845 
1846 

1847 


1848 


1849 


1850 


1851 


1852 


1853 
1854 


1855 


1856 


1857 
1858 


1859 


1860 


1861 


1862 


1863 


Months 
and 
Days. 


1864 
1865 


m  p 

m 
m 
m  p 

m 
m 

m  T 
i)  T 

m 
m 
m  p 
i)  p 

m 

m 

e  p 

(D  P 

m 
m  T 
m  T 

m 

e  p 
§)  p 
m  p 
i)  p 
m  T 

i)  T 

m  p 

i)  p 
m 
e  p 

m  p 

i)  T 

i)  T 
i)  P 
# 
€)P 

f)P 
m  T 

It 
i)  P 


Nov.  14 
April  25 
Oct.  20 
March  31 
Sept.  24 
Oct.  9 
Marchl9 
Sept.  13 
Sept.  27 
Feb.  23 
March  9 
Sept.  2 
Feb.  12 
Aug.  7 
Jan.  17 
July  13 
July  28 
Jan.  7 
July  1 
Dec.  11 
Dec.  26 
June  21 
May  12 
Nov.  4 
May  2 
May  16 
Oct.  25 
April  20 
Sept.  29 
Oct.  13 
Sept.  18 
Feb.  27 
March  15 
Aug.  24 
Feb.  17 
July  29 
Aug.  13 
Feb.  7 
July  18 
Aug.  1 
Jan.  11 
Julys 
Dec.  17 
Dec.  31 
June  12 
Dec.  6 
Dec.  21 
May  17 
June  2 
Nov.  25 
May  6 
April  11 
Oct.  4 


Tinae. 


I  M 

5h  A 
S^M 
9h  A 

3  A 
9iM 
9^  A 
6k  M 

10  M 
l^M 
1  M 
5i  A 
61  M 

10  A 

5  A 
7iM 
2i  A 
6^M 
3|  A- 
4  M 

1  A 

6  M 

4  A 
9i  A 
4iM 
2iM 
8  M 
9iM 

4  M 

Hi  A 

6  M 
IDA  A 
Oh  A 

n  A 

II  M 

9i  A 
4h  A 
2iM 

2  A 
5i  A 
S^M 
2  M 
S^M 
2i  A 
6|M 

8  M 
5^M 

5  A 
0  M 

9  M 
0|M 
5  M 

11  A 


Chap. 


I. 


THE  TERRESTRIiVL  GLOBE. 


251 


Months 

tn 

Months 

and 

Time. 

ra 
a> 

and 

Time. 

Days. 

Days. 

1865 

Oct.  19 

 _ 

5  A 

1882 

# 

Nov.  11 

0  M 

1866 

March  16 

10  A 

1883 

®  P 

April  22 

Merid. 

f)  T 

March  31 

5  M 

i)  P 

Oct.  16 

7^  M 

w  J- 

Sept.  24 

2^  A 

Oct.  31 

0i|  M 

Oct.  8 

5^  A 

1884 

# 

March  27 

6  M 

1867 

March  6 

10  M 

•  T 

April  10 

Merid 

i)  p 

March  20 

9  M 

®  T 

Oct.  4 

10;^  A 

i)  p 

Sept.  14 

1  M 

Oct.  19 

1  M 

1868 

Feb.  23 

2^  A 

1885 

f)  P 

March  30 

5  A 

Aug.  18 

5^M 

dD  P 

Sept.  24 

1869 

dD  " 

.Tan.  28 

IJ M  • 

1886 

Aug.  29 

H  A 

dllL)  -t^  ■ 

July  23 

2  A 

1887 

<ID  P 

Feb  8 

10^  M 

Aug.  7. 

10  A 

(D  P 

Aug.  3 

9  A 

1870 

€)  T 

Jan  17 

3  A 

Aug.  19 

6  M 

D  T 

July  12 

11  A 

1888 

f)  T 

Jan.  28 

lU  A 

Dec.  22 

0|  A 

€>  T 

July  23 

6  M 

1871 

€)  P 

Jan.  6 

9|  A 

1889 

f)  P 

.Tan.  17 

S^M 

w 

June  18 

2iM 

(D  P 

July  12 

9  A 

Hit'  Jr 

July  2 

1^  A 

@ 

Dec.  22 

1  A 

Dec.  12 

4^M 

1890 

i)  P 

June  23 

6  M 

1872 

€)  P 

May  22 

Hi  A 

June  17 

10  M 

w 

June  6 

3iM 

dD  P 

Nov.  26 

2  A 

1®  p 

Nov.  15 

5|  M 

1891 

dD  T 

May  23 

7  A 

1873 

w  J- 

May  12 

ll^M 

% 

June  6 

4i  A 

May  26 

9i  M 

dD  T 

Nov.  16 

0|  M 
ll|  A 

Nov.  4 

4i  A 

1892 

(D  P 

May  11 

1874 

®  P 

May  1 

4^  A 

dD  T 

Nov.  4 

4|  A 

w 

Oct.  10 

ii|m 

1893 

April  16 

3  A 

C!  P 

Oct.  25 

8  M 

1894 

dD  P 

March  21 

2i  A 

1875 

April  6 

7  M 

April  6 

4^  M 

Sept.  29 

1^  A 

dD  P 

Sept  15 

4:1  M 

1876 

•JD  P 

March  10 

6|M 

Sept.  29 

5^  M 

H)  P 

Sept.  3 

9^  A 

1895 

dD  T 

March' 11 

4  M 

1877 

ID  T 

Feb.  27 

7^  A 

March  26 

10  M 

MarchlS 

3  M 

Aug.  20 

0^  A 

Aug.  9 

5  M 

dD  T 

Sept.  4 

6  M 

w)  1 

Aug.  23 

11^  A 

1896 

dD  P 

Feb.  28 

8  A 

1878 

ID  P 

Feb.  17 

11^  M 

0 

Aug.  9 

4k  M 

w 

July  29 

H  A 

dD  P 

Aug.  23 

1  M 

(It;  jp 

Aug.  13 

Ok  M 

1897 

No 

visible  Eclipse. 

1879 

Jan.  22 

Merid. 

1898 

dD  P 

Jan.  8 

O^M 

w 

July  19 

9  M 

Jan.  22 

8  M 

W  " 

Dec.  28 

4^  A 

dD  P 

July  3 

H  A 

1880 

Jan.  11 

11  A 

dD  T 

Dec.  27 

12  A 

i)  T 

Tiinp  22 

2  A 

1899 

Jan. 11 

11  A 

€)  T 

Dec.  16 

4  A 

m 

June  8 

7  M 

Dec.  31 

2  A 

m  T 

June  23 

2^  A 

1881 

May  28 

0  M 

dD  P 

Dec.  17 

H  M 

June  12 

71  M 

1900 

m 

May  28 

34  A 

i)  P 

Dec.  5 

5^  A 

dDP 

June  13 

4  M 

1882 

May  17 

8  M 

Nov.  22 

8  M 

252 


PROBLEMS  PERFORMED  BY 


Part  III. 


PROBLEM  LV. 

To  find  the  time  of  the  year  when  the  Sun  or  Moon  will  be  liable  to 

be  eclipsed. 

Rule.  Find  the  place  of  the  moon's  nodes,  the  time  of  new 
moon,  and  the  sun's  longitude  at  that  time,  by  an  ephemeris  ;* 
then  if  the  sun  be  within  IT  degrees  of  the  moon's  node,  there 
will  be  an  eclipse  of  the  sun. 

2.  Find  the  place  of  the  moon's  nodes,  the  time  of  full  moon, 
and  the  sun's  longitude  at  that  time,  by  an  ephemeris  ;  then  if  the 
sun's  longitude  be  within  12  degrees  of  the  moon's  node,  there 
will  be  an  eclipse  of  the  moon. 

Or,  without  the  ephemeris. 

The  mean  annual  variation  of  the  moon's  nodes  is  19°  19'  44" 
(page  147)  and  the  place  of  the  node  for  the  first  of  January 
1825  being  29°  42'  in  / ,  its  place  for  any  other  time  may  there- 
fore be  found. 

The  time  of  new  moon  may  be  found  as  directed  at  page  176, 
and  the  sun's  longitude  is  the  sun's  place  in  the  ecliptic.f  The 
rest  may  be  found  as  above. 

Examples.  1.  On  the  21st  of  May,  1826,  there  will  be  a 
full  moon,  at  which  time  the  place  of  the  Moon's  node  is  2°  56' 
in  /,  and  the  sun's  longitude  ^  29*^  58';  will  an  eclipse  of  the 
moon  happen  at  that  time  ? 

Answer.  Here  the  sun's  longitude  is  within  3  degrees  nearly  of  the  moon's  node, 
therefore  there  will  be  an  echpse  of  the  moon. — When  the  sun  is  in  one  of  the 
moon's  nodes  at  the  time  of  full  moon,  the  moon  is  in  the  other  node,  and  the 
earth  is  directly  between  them. 

2.  It  appears  from  the  table  (page  181)  that  there  will  be  a 
new  moon  on  the  6th  of  May,  1826,  at  which  time  the  place  of 
the  moon's  node  will  be  t  3°  45',  and  the  sun's  longitude  ^  15°  58' ; 
will  there  be  an  echpse  of  the  sun  at  that  time  ? 

3.  There  will  be  a  new  moon  on  the  5th  of  June,  1826,  at 
which  time  the  place  of  the  moon's  node  will  be     2°  8'  and  the 


*  White's  Ephemeris,  or  the  Nautical  Almanac. 

I  The  moon's  longitude  may  be  found  thus :  multiply  12°  11'  Q''  by  the  moon*s 
age  {see  pages  91  and  176),  the  product  will  give  the  number  of  degrees  by  which 
^   the  moon's  longitude  exceeds  that  of  the  sun. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


253 


sun's  longitude  n  14"  27' ;  will  there  be  an  eclipse  of  the  sun  at 
that  time  ? 

4.  On  the  14th  of  November  1826,  there  will  be  a  full  moon, 
at  which  time  the  place  of  the  moon's  node  will  be  ttl  23 '  34',  and 
the  sun's  longitude  tri  21"  47':  will  there  be  an  eclipse  of  the 
moon  at  that  time  ? 

5.  On  the  28th  of  November  1826,  there  will  be  a  new  moon 
at  which  time  the  place  of  the  moon's  node  is  rn.  22"  44',  and  the 
sun's  longitude  f  6"  46' ;  will  there  be  an  eclipse  of  the  sun  at 
that  time  ? 

6.  On  the  28th  of  December  1826,  there  will  be  a  new  moon, 
at  which  time  the  place  of  the  moon's  node  is  yxi  21"  14',  and  the 
sun's  longitude  V3  6°  44' ;  will  there  be  an  eclipse  of  the  sun  at 
that  time  ? 


PROBLEM  LVI. 

To  explain  the  phenomenon  of  the  harvest  moon. 

Definition  1.  The  harvest  moon,  in  north  latitude,  is  the 
full  moon  which  happens  at,  or  near,  the  time  of  the  autumnal 
equinox ;  for,  to  the  inhabitants  of  north  latitude,  whenever  the 
moon  is  in  Pisces  or  Aries  (and  she  is  in  these  signs  twelve  times 
in  a  year,)  there  is  very  little  difference  between  her  times  of  ris- 
ing for  several  nights  together,  because  her  orbit  is  at  these  times 
nearly  parrallel  to  the  horizon.  This  peculiar  rising  of  the  moon' 
passes  unobserved  at  all  other  times  of  the  year  except  m  Sep- 
tember and  October;  for  there  never  can  be  a  full  moon  except 
the  sun  be  directly  opposite  to  the  moon  ;  and  as  this  particular 
rising  of  the  moon  can  only  happen  when  the  moon  is  in  ^  Pices 
or  ^  Aries,  the  sun  must  necessarily  be  either  in  Virgo  or  =^ 
Libra  at  that  time,  and  these  signs  answer  to  the  months  of  Sep- 
tember and  October. 

Definition  2.  The  harvest  moon,  in  south  latitude,  is  the  full 
moon  which  happens  at,  or  near,  the  time  of  the  vernal  equinox ; 
for,  to  the  inhabitants  of  south  latitude,  whenever  the  moon  is  in 
V!^  Virgo  or  Libra  (and  she  is  in  these  signs  twelve  times  in  the 
year),  her  orbit  is  nearly  parallel  to  the  horizon ;  but  when  the 
full  moon  happens  in  nj^  Virgo  or  =^  Libra,  the  sun  must  be  either 
in  ^  Pisces  or  ^  Aries.  Hence  it  appears  that  the  harvest  moons 
are  just  as  regular  in  south  latitude  as  they  are  in  north  latitude, 
only  they  happen  at  contrary  times  of  the  year. 


254 


PROBLEMS  PERFORMED  BY 


Part  III. 


Rule  for  performing  the  problem. — 1.  Fo7^  north  latitude. 
Elevate  the  north  pole  to  the  latitude  of  the  place,  put  a  patch  or 
make  a  mark  in  the  ecliptic  on  the  point  Aries,  and  upon  every 
twelve*  degrees  preceding  and  following  that  point,  till  there  be 
ten  or  eleven  marks ;  bring  that  mark  which  is  nearest  to  Pisces 
to  the  eastern  edge  of  the  horizon,  and  set  the  index  to  12 ;  turn 
the  globe  westward  till  the  other  marks  successively  come  to  the 
horizon,  and  observe  the  hours  passed  over  by  the  index  ;  the  in- 
tervals of  time  between  the  marks  coming  to  the  horizon  will 
show  the  diurnal  difference  of  time  between  the  moon's  rising. 
If  these  marks  be  brought  to  the  western  edge  of  the  horizon  in 
the  same  manner,  you  will  see  the  diurnal  difference  of  time  be- 
tween the  moon's  setting ;  for,  when  there  is  the  smallest  differ- 
ence between  the  times  of  the  moon's  rising,f  there  will  be  the 
greatest  difference  between  the  times  of  her  setting ;  and,  on  the 
contrary,  when  there  is  the  greatest  difference  between  the  times 
of  the  moon's  rising,  there  will  be  the  least  difference  between 
the  times  of  her  setting. 

Note.  As  the  moon's  nodes  vary  their  position  and  form  a  complete  revolution 
in  about  nineteen  years,  there  will  be  a  regular  period  of  all  the  varieties  M'hich  can 
happen  in  the  rising  and  setting  of  the  moon  during  that  time.  The  following  table 
(extracted  from  Ferguson's  Astronomy)  shows  in  what  years  the  harvest  moons 
are  the  least  and  most  beneficial,  with  regard  to  the  times  of  their  rising  from  1823 
to  I860.  The  colums  of  years  under  the  letter  L  are  those  in  which  the  harvest 
moons  are  least  beneficial,  because  they  fall  about  the  descending  node ;  and  those 
under  M  are  the  most  beneficial,  because  they  fall  about  the  ascending  node. 


L       L  L  L 

1826  1831  1845  1849 

1827  1832  1846  1850 

1828  1833  1847  1851 

1829  1834  1848  1852 

1830  1844 


M       M  M  M 

1823  1837  1842  1856 

1824  1838  1843  1857 

1825  1839  1853  1858 

1835  1840  1854  1859 

1836  1841  1855  1860 


2.  For  south  latitude.  Elevate  the  south  pole  to  the  latitude  of 
the  place,  put  a  patch  or  make  a  mark  on  the  ecliptic  on  the  point 
Libra,  and  upon  every  twelve  degrees  preceding  and  following 
that  point,  till  there  be  ten  or  eleven  marks ;  bring  that  mark 
which  is  nearest  to  Virgo,  to  the  eastern  edge  of  the  horizon,  and 


*  The  reason  why  you  mark  every  12  degrees  is,  that  the  moon  gains  12°  IF  of 
the  sun  in  the  ecliptic  every  day  (see  the  2d  note,  p.  80.) 

t  At  London,  when  the  moon  rises  in  the  point  Aries,  the  ecliptic  at  that  point 
makes  an  angle  of  only  15  degrees  with  the  horizon,  but  when  she  sets  in  the 
point  Aries,  it  makes  an  angle  of  62  degrees :  and  when  the  moon  rises  in  the 
point  Libra,  the  ecUptic,  at  that  point,  makes  an  angle  of  62  degrees  with  the  ho- 
rizon ;  but,  when  she  sets  in  the  point  Libra,  it  only  makes  an  angle  of  15  degrees 
with  the  horixon. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


255 


set  the  index  to  12  ;  turn  the  globe  westward  till  the  other  marks 
successively  come  to  the  horizon,  and  observe  the  hours  passed 
over  by  the  index  ;  the  intervals  of  time  between  the  marks 
coming  to  the  horizon,  will  be  the  diurnal  difference  of  time 
between  the  moon's  rising,  &c.  as  in  the  foregoing  part  of  the 
problem.* 

PROBLEM  LVII. 

The  day  and  Iwur  of  an  eclipse  of  any  one  of  the  satellites  of 
Jupiter  being  given,  to  find  upon  the  globe  all  those  places  where 
it  will  be  visible. 

Rule.  Find  the  sun's  declination  for  the  given  day,  and  elevate 
the  pole  to  that  declination  ;  bring  the  place  at  which  the  hour 
is  given  to  the  brass  meridian,  and  set  the  index  of  the  hour 
circle  to  12 ;  then,  if  the  given  time  be  before  noon,  turn  the 
globe  westward  as  many  hours  as  it  wants  of  noon ;  if  after 
noon,  turn  the  globe  eastward  as  many  hours  as  it  is  past  noon  ; 
fix  the  globe  in  this  position  :  Then, 

1.  If  Jupiter  rise  after  the  sun-\,  that  is  if  he  be  an  evening  star, 
draw  a  line  along  the  eastern  edge  of  the  horizon  with  a  black  lead 
pencil,  this  line  will  pass  over  all  places  on  the  earth  where  the 
sun  is  setting  at  the  given  hour ;  turn  the  globe  westward  on  its 
axis  till  as  many  degrees  of  the  equator  have  passed  under  the 
brass  meridian  as  are  equal  to  the  difference  between  the  sun's 
and  Jupiter's  right  ascension ;  keep  the  globe  from  revolvino;  on 
its  axis,  and  elevate  the  pole  as  many  degrees  above  the  horizon 
as  are  equal  to  Jupiter's  declination,  then  draw  an  other  line  with 
a  pencil  along  the  eastern  edge  of  the  horizon :  the  eclipse  will 
be  visible  to  every  place  between  these  lines,  viz.  from  the  time 
of  the  sun's  setting  to  the  time  of  Jupiter's  setting. 

2.  If  Jupiter  rise  before  the  sunX,  that  is,  if  he  be  a  morning  star, 
draw  a  line  along  the  western  edge  of  the  horizon  with  a  black  lead 


*  This  solution  is  on  a  supposition  that  the  moon  keeps  constantly  in  the 
ecliptic,  which  is  sufficiently  accurate  for  illustrating  the  problem.  Otherwise  the 
latitude  and  longitude  of  the  moon,  or  her  right  ascension  and  declination,  maybe 
taken  from  the  Ephemeris,  at  the  time  of  full  moon,  and  a  few  days  preceding  and 
following  it ;  her  place  will  then  be  truly  marked  on  the  globe. 

t  Jupiter  rises  after  the  sun,  when  his  longitude  is  greater  than  the  sun's 
longitude. 

X  Jupiter  rises  before  the  sun,  when  his  longitude  is  less  than  the  sun's 
longitude. 


^56 


PROBLEMS  PERFORMED  BY 


Part  III. 


pencil,  this  line  will  pass  over  all  places  of  the  earth  where  the 
sun" is  rising  at  the  given  hour;  turn  the  globe  eastward  on  its 
axis  till  as  many  degrees  of  the  equator  have  passed  under  the 
brass  meridian  as  are  equal  to  the  difference  between  the  sun's 
and  Jupiter's  right  ascension  ;  keep  the  globe  from  revolving  on 
its  axis,  and  elevate  the  pole  as  many  degrees  above  the  horizon 
as  are  equal  to  Jupiter's  declination,  then  draw  an  other  line  with 
a  pencil  along  the  western  edge  of  the  horizon  :  the  eclipse  will 
be  visible  to  every  place  between  these  lines,  viz.  from  the  time 
of  Jupiter's  rising  to  the  time  of  the  sun's  rising. 

Examples.  1.  On  the  13th  of  January,  1805,  there  was  an 
immersion  of  the  first  satellite  of  Jupiter  at  9  m.  3.  sec.  past  five 
o'clock  in  the  morning  at  Greenwich  ;  where  was  it  visible  ? 

Jinswer,  In  this  example  the  longitude  of  the  sun  exceeds  the  longitude  of 
Jupiter,  therefore  Jupiter  was  a  morning  star,  his  declination  being  19°  16'  S.  and 
his  longitude  7  signs  29'  46',  by  the  Nautical  Almanac  :  his  right  ascension  and 
the  sun's  right  ascension  may  be  found  by  the  globe  ;  for,  if  Jupiter's  longitude  in 
the  ecliptic  be  brought  to  the  brass  meridian,  his  place  will  stand  under  the  degree 
of  his  declination  ;*  and  his  right  ascension  will  be  found  on  the  equator,  reckoning 
from  Aries.  This  ecUpse  was'visible  at  Greenwich,  the  greater  part  of  Europe, 
the  west  of  Africa,  Cape  Verd  Islands,  &c. 

2.  On  the  18th  of  January,  1826,  at  4  m.  49  sec.  past  three 
o'clock  in  the  morning  at  Greenwich,  there  will  be  an  immersion 
of  the  first  satellite  of  Jupiter ;  where  will  the  eclipse  be  visible  ? 
Jupiter's  longitude  at  that  time  being  5  signs  13°  51'  and  his 
declination  7°  33'  north. 

3.  On  the  13th  of  April,  1826,  at  5  m.  5  sec.  past  four  o'clock 
in  the  morning,  at  Greenwich,  there  will  be  an  emersion  of  the 
first  satellite  of  Jupiter ;  where  will  the  eclipse  be  visible  ? 
Jupiter's  longitude  at  that  time  being  5  signs  4°  55'  and  his 
declination  11°  north. 

4.  On  the  20th  of  November,  1826,  at  31  min.  13  sec.  past 
nine  o'clock  in  the  morning,  at  Greenwich,  there  will  be  an 
immersion  of  the  second  satellite  of  Jupiter ;  where  will  the 
eclipse  be  visible  ?  Jupiter's  longitude  at  that  time  being  6  signs 
T  38',  and  his  declination  1°  57'  north. 


♦  This  is  on  supposition  that  Jupiter  moves  in  the  ecliptic,  and  as  he  deviates  but 
little  therefrom,  the  solution  by  this  method  will  be  sufficiently  accurate.  To 
know  if  an  eclipse  of  any  one  of  the  satellites  of  Jupiter  will  be  visible  at  any 
place,  we  are  directed  by  the  Nautical  Almanac  to  "  find  whether  Jupiter  be  88° 
above  the  horizon  of  the  place,  and  the  sun  as  much  below  it." 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


PROBLEM  LVIII. 

To  place  the  terrestrial  globe  in  the  sunshine,  so  that  it  may 
represent  the  natural  position  of  the  earth. 

Rule.  If  you  have  a  meridian  line*  drawn  upon  a  horizontal 
plane,  set  the  north  and  south  points  of  the  wooden  horizon  of  the 
globe  directly  over  this  line  ;  or,  place  the  globe  directly  north 
and  south  by  the  mariner's  compass,  taking  care  to  allow  for  the 
variation  ;  bring  the  place  in  which  you  are  situated  to  the  brass 
meridian,  and  elevate  the  pole  to  its  latitude ;  then  the  globe  will 
correspond  in  every  respect  with  the  situation  of  the  earth  itself. 
The  poles,  meridians,  parallel  circles,  tropics,  and  all  the  circles 
on  the  globe,  will  correspond  with  the  same  imaginary  circles  in 
the  heavens ;  and  each  point,  kingdom,  and  state,  will  be  turned 
towards  the  real  one,  which  it  represents. 

While  the  sun  shines  on  the  globe,  one  hemisphere  will  be  en- 
lightened, and  the  other  will  be  in  the  shade:  thus,  at  one  view, 
may  be  seen  all  places  on  the  earth  which  have  day,  and  those 
which  have  night. f 

If  a  needle  be  placed  perpendicularly  in  the  middle  of  the  en- 
lightened hemisphere,  (which  must  of  course  be  upon  the  parallel 
of  the  sun's  declination  for  the  given  day,)  it  will  cast  no  shadow, 
which  shows  that  the  sun  is  vertical  at  that  point ;  and  if  a  line 
be  drawn  through  this  point  from  pole  to  pole,  it  will  be  the 
meridian  of  the  place  where  the  sun  is  vertical,  and  every  place 
upon  this  line  will  have  noon  at  that  time ;  all  places  to  the  west 
of  this  line  will  have  morning,  and  all  places  to  the  east  of  it  af- 
ternoon. Those  inhabitants  who  are  situated  on  the  circle  which 
is  the  boundary  between  light  and  shade,  to  the  westward  of  the 
meridian  where  the  sun  is  vertical,  will  see  the  sun  rising;  those 
in  the  same  circle  to  the  eastward  of  this  meridian  will  see  the  sun 
setting ;  those  inhabitants  towards  the  north  of  the  circle,  which 
is  the  boundary  between  light  and  shade,  will  perceive  the  sun  to 
the  southward  of  them,  in  the  horizon ;  and  those  who  are  in  the 


*  A  a  meridian  line  is  useful  for  fixing  a  horizontal  dial,  and  for  placing  a  globe 
directly  north  and  sonlh,  &c.  the  different  methods  of  drawing  a  line  of  this  kind 
will  precede  the  problems  on  dialling. 

t  For  this  part  of  the  problem  it  would  be  more  convenient  if  the  globe  could  be 
properly  supported  without  the  frame  of  it,  because  the  shadow  of  its  stand,  and 
that  of  its  horizon,  will  darken  several  parts  of  the  surface  of  the  globe,  which  Would 
otherwise  be  enlightened^ 


258 


PROBLEMS  PERFORMED  BY 


Part  III. 


same  circle  towards  the  south,  will  see  the  sun  in  a  similar  man- 
ner to  the  north  of  them. 

If  the  sun  shine  beyond  the  north  pole  at  the  given  time,  his 
declination  is  as  many  degrees  north  as  he  shines  over  the  pole  ; 
and  all  places  at  that  distance  from  the  pole  will  have  constant 
day,  till  the  sun's  declination  decreases,  and  those  at  the  same  dis- 
tance from  the  south  pole  will  have  constant  night. 

If  the  sun  do  not  shine  so  far  as  the  north  pole  at  the  given  time, 
his  declination  is  as  many  degrees  south  as  the  enlightened  part 
is  distant  from  the  pole  ;  and  all  places  within  the  shade  near  the 
pole,  will  have  constant  night,  till  the  sun's  declination  increases 
northward.  While  the  globe  remains  steady  in  the  position  it 
was  first  placed  when  the  sun  is  westward  of  the  meridian,  you 
may  perceive  on  the  east  side  of  it,  in  what  manner  the  sun  grad- 
ually departs  from  place  to  place  as  the  night  approaches ;  and 
when  the  sun  is  eastward  of  the  meridian,  you  may  perceive  on 
the  western  side  of  it,  in  what  manner  the  sun  advances  from 
place  to  place  as  the  day  approaches. 


PROBLEM  LIX. 

The  latitude  of  a  place  being  given,  to  fold  the  hour  of  the  day  at 
any  time  when  the  sun  shines. 

Rule.  I.  Place  the  nOrth  and  south  points  of  the  horizon  of 
the  globe  directly  north  and  south  upon  a  horizontal  plane,  by  a 
meridian  line,  or  by  a  mariner's  compass,  allowing  for  the  varia- 
tion, and  elevate  the  pole  to  the  latitude  of  the  place  ;  then,  if  the 
place  be  in  north  latitude,  and  the  sun's  declination  be  north, 
the  sun  will  shine  over  the  north  pole  ;  and  if  a  long  pin  be  fixed 
perpendicularly  in  the  direction  of  the  axis  of  the  earth,  and  in  the 
centre  of  the  hour  circle,  its  shadow  will  fall  upon  the  hour  of 
the  day,  the  figure  XII  of  the  hour  circle  being  first  set  to  the 
brass  meridian.  If  the  place  be  in  north  latitude,  and  the  sun's 
declination  be  above  ten  degrees  south,  the  sun  will  not  shine  up- 
on the  hour  circle  at  the  north  pole. 

Rule  2.  Place  the  globe  due  north  and  south  upon  a  horizon- 
tal plane,  as  before,  and  elevate  the  pole  to  the  latitude  of  the 
place ;  find  the  sun's  place  in  the  ecliptic,  bring  it  to  the  brass 
meridian,  and  set  the  index  of  the  hour  circle  to  XII ;  stick  a  nee- 
dle perpendicularly  in  the  sun's  place  in  the  ecliptic,  and  turn  the 
globe  on  its  axis  till  the  needle  casts  no  shadow ;  fix  the  globe  in 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


25» 


this  position  and  the  index  will  show  the  hour  before  12  in  the 
morning,  or  after  12  in  the  afternoon. 

Rule  3,  Divide  the  equator  into  24  equal  parts  from  the  point 
Aries,  on  which  place  the  number  VI ;  and  proceed  westward 
VII,  VllI,  IX,  X,  XI,  XII,  I,  II,  III,  IV,  V,  VI,  which  will  fall 
upon  the  point  Libra,  VII,  VIII,  IX,  X,  XI,  XII,  I,  II,  III,  IV, 
V* ;  elevate  the  pole  to  the  latitude,  place  the  globe  due  north 
and  south  upon  a  horizontal  plane,  by  a  meridian  line,  or  a  good 
mariner's  compass,  allowing  for  the  variation,  and  bring  the  point 
Aries  to  the  brass  meridian  ;  then  observe  the  circle  which  is  the 
boundary  between  light  and  darkness  westward  of  the  brass  me- 
ridian ;  and  it  will  intersect  the  equator  in  the  given  hour  in  the 
morning ;  but,  if  the  same  circle  be  eastward  of  the  meridian,  it 
will  intersect  the  equator  in  the  given  hour  in  the  afternoon.  • 

Or,  Having  placed  the  globe  upon  a  true  horizontal  plane,  set 
it  due  north  and  south  by  a  meridian  line  ;  elevate  the  pole  to  the 
latitude,  and  bring  the  point  Aries  to  the  brass  meridian,  as  be- 
fore ;  then  tie  a  small  string,  with  a  noose,  round  the  elevated 
pole,  stretch  its  other  end  beyond  the  globe^  and  move  it  so  that 
the  shadow  of  the  string  may  fall  upon  the  depressed  axis :  at 
that  instant  its  shadow  upon  the  equator  will  give  the  hour.f 


PROBLEM  LX. 

To  find  the  sun^s  altitude^  hy  placing  the  globe  in  the  sunshine. 

Rule.  Place  the  globe  upon  a  truly  horizontal  plane,  stick  a  nee- 
dle perpendicularly  over  the  north  pole  J,  in  the  direction  of  the 
axis  of  the  globe,  and  turn  the  pole  towards  the  sun,  so  that  the 
shadow  of  the  needle  may  fall  upon  the  middle  of  the  brass 


*  On  Mams'  globes  the  antarctic  circle  is  thus  divided,  by  which  this  problem 
may  be  solved. 

t  The  learner  must  remember  that  the  time  shown  in  this  problem  is  solar  time, 
as  shovi^n  by  a  sun  dial ;  and,  therefore,  to  agree  with  a  good  clock  or  watch,  it 
must  be  corrected  by  a  table  of  equation  of  time.  See  a  table  of  this  kind  among 
the  succeeding  problems. 

X  It  would  be  an  improvement  on  the  globes  were  our  instrument-makers  to  drill 
a  very  small  hole  in  the  brass  meridian  over  the  north  pole. 


260 


PROBLEMS  PERFORMED  BY 


Part  III. 


meridian  :  then  elevate  or  depress  the  pole  till  the  needle  casts  no 
shadow  ;  for  then  it  will  point  directly  to  the  sun  ;  the  elevation 
of  the  polq  above  the  horizon  will  be  the  sun's  altitude. 


PROBLEM  LXI. 

To  find  the  surCs  declination,  his  place  in  the  ecliptic,  and  his 
azimuth,  hy  placing  the  globe  in  the  sunshine. 

Rule.  Place  the  globe  upon  a  truly  horizontal  plane,  in  a 
north  and  south  direction  by  a  meridian  hne,  and  elevate  the  pole 
to  the  latitude  of  the  place ;  then,  if  the  sun  shine  beyond  the 
north  pole,  his  declination  is  as  many  degrees  north  as  he  shines 
over  the  pole  ;  if  the  sun  do  not  shine  so  far  as  the  north  pole,  his 
declination  is  as  many  degrees  south  as  the  enlightened  part  is 
distant  from  the  pole.  The  sun's  declination  being  found,  his 
place  may  be  determined  by  Problem  XX. 

Stick  a  needle  in  the  parallel  of  the  sun's  declination  for  the 
given  day*,  and  turn  the  globe  on  its  axis  till  the  needle  casts  no 
shadow :  fix  the  i;lobe  in  this  position,  and  screw  the  quadrant 
of  altitude  over  the  latitude  ;  bring  the  graduated  edge  of  the 
quadrant  to  coincide  with  the  sun's  place,  or  the  point  v^^here 
the  needle  is  fixed,  and  the  degree  on  the  horizon  will  show  the 
azimuth. 


PROBLEM  LXn. 

To  draw  a  meridian  line  upon  a  horizontal  plane,  and  to  determine 
the  four  cardinal  points  of  the  horizon. 

Rule  L  Describe  several  circles  from  the  centre  of  the  hori- 
zontal plane,  in  which  centre  fix  a  straight  wire  perpendicular  to 
the  plane ;  mark  in  the  morning  where  the  end  of  the  shadow 
touches  one  of  the  circles  ;  in  the  afternoon  where  the  end  of  the 
shadow  touches  the  same  circle ;  divide  the  arc  of  the  circle  contained 


♦  On  Jidams^  globes  the  torrid  zone  is  divided  into  degrees  by  dotted  lines,  so 
that  the  parallel  of  the  sun's  declination  is  instantly  found  :  in  using  other  globes, 
observe  the  declination  on  the  brass  meridian,  and  stick  a  needle  perpendicularly 
in  the  globe  under  that  degree. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


261 


between  these  two  points  into  two  equal  parts  ;  a  line  drawn 
from  the  point  of  division  to  the  centre  of  the  plane  will  be  a  true 
meridian,  or  north  and  south  line  ;  and  if  this  line  be  bisected  by 
a  perpendicular,  that  perpendicular  will  be  an  east  and  west  line  : 
thus  you  will  have  the  four  cardinal  points  ;  but  to  be  very  ex- 
act, the  plane  must  be  truly  horizontal,  the  wire  must  be  exactly 
perpendicular  to  the  plane,  and  the  extremity  of  its  shadow  must 
be  compared,  not  only  upon  one  of  the  circles,  as  above  described^ 
but  upon  several  of  them. 

Rule  2.  Fix  a  strong  straight  wire  sharp  pointed  at  the  top 
in  the  centre  of  your  plane,  nearly  perpendicular ;  place  one  end 
of  a  wooden  ruler  on  the  top  of  the  wire,  and  with  a  sharp  pointed 
iron  pin,  or  wire,  in  the  other  end  of  the  ruler,  describe  an 
arc  of  a  circle  ;  take  off  the  ruler  from  the  top  of  the  wire,  and 
observe  at  two  different  times  of  the  day,  when  the  shadow  of  the 
top  of  the  wire  falls  upon  the  arc  of  the  circle  described  by  the 
ruler ;  mark  the  two  points,  and  divide  the  arc  between  them  into 
two  equal  parts,  and  draw  a  line  from  the  point  of  bisection  to 
the  centre  of  your  plane :  this  will  be  a  meridian  line. 

Rule  3.  Hang  up  a  plumb-line  in  the  sunshine,  so  that  it  may 
cast  a  shadow  of  a  considerable  length,  upon  the  horizontal  plane, 
on  which  you  intend  to  draw^  your  meridian  line  ;  draw  a  line 
along  this  shadow  upon  the  plane,  while  at  the  same  time  a  per- 
son takes  the  altitude  of  the  sun  correctly  with  a  quadrant,  or 
some  other  instrument  answering  the  same  purpose ;  then,  by 
knowing  the  latitude  of  the  place,  the  day  of  the  month,  and  of 
course  the  sun's  declination,  together  with  his  altitude ;  find  the 
azimuth,  from  the  north,  by  spherical  trigonometry,  and  subtract 
it  from  180°  :  make  an  angle,  at  any  point  of  the  line  which  was 
drawn,  upon  your  plane,  equal  to  the  number  of  degrees  in  the 
remainder,  and  that  will  point  out  the  true  meridian.  See  Keith's 
Trigonometry,  fourth  edition,  page  315. 

Rule  4.  Take  the  sun's  altitude  with  an  octant,  sextant,  or 
quadrant  at  any  convenient  time  in  the  forenoon,  and  note  the 
time  by  a  good  watch.  Compute  by  spherical  trigonometry  the 
time  corresponding  to  the  correct  altitude,  by  which  correct  the 
error  of  the  watch :  and  when  it  is  noon  by  the  watch  thus  cor- 
rected, draw  a  meridian  line  by  the  shadow  of  a  vertical  line  if 
the  sun  shines. 


262 


PROBLEMS  PERFORMED  BY 


Part  III. 


PROBLEM  LXIII. 
To  make  a  horizontal  dial  for  any  latitude. 

Definitions  and  Observations. — Dialling,  or  the  art  of 
constructing  dials,  is  founded  entirely  on  astronomy  ;  and,  as  the 
art  of  measuring  time  is  of  the  greatest  importance,  so  the  art  of 
dialling  was  formerly  held  in  the  highest  esteem,  and  the  study  of 
it  was  cultivated  by  all  persons  who  had  any  pretensions  to  sci- 
ence. Since  the  invention  of  clocks  and  watches,  dialling  has  not 
been  so  much  attended  to,  though  it  will  never  be  entirely  neg- 
lected ;  for,  as  clocks  and  watches  are  liable  to  stop  and  go  wrong, 
that  unnerring  instrument,  a  true  sun-dial,  is  used  to  correct  and 
to  regulate  them. 

Suppose  the  globe  of  the  earth  to  be  transparent  (as  represent- 
ed by  Fig.  4.  in  Plate  11.)  with  the  hour  circles,  or  meridians,  &c. 
drawn  upon  it,  and  that  it  revolves  round  a  real  axis  ns,  which  is 
opaque  and  casts  a  shadow  ;  it  is  evident  that,  whenever  the  edge 
of  the  plane  of  any  hour  circle  or  meridian  points  exactly  to  the 
sun,  the  shadow  of  the  axis  will  fall  upon  the  opposite  hour  cir- 
cle or  meridian.  Now,  if  we  imagine  any  opaque  plane  to  pass 
through  the  centre  of  this  transparent  globe,  the  shadow  of  half 
the  axis  ne  will  always  fall  upon  one  side  or  other  of  this  inter- 
secting plane. 

Let  ABCD  represent  the  plane  of  the  horizon  of  London,  bn 
the  elevation  of  the  pole  or  latitude  of  the  place :  so  long  as  the 
sun  is  above  the  horizon,  the  shadow  of  the  upper  half  ne  of  the 
axis  will  fall  somewhere  upon  the  upper  side  of  the  plane  abcd. 
When  the  edge  of  the  plane  of  any  hour  circle,  as  f,  g,  h,  i,  k,  l, 
M,  o,  points  directly  to  the  sun,  the  shadow  of  the  axis,  which  axis 
is  coincident  with  this  plane,  marks  the  respective  hour  line 
upon  the  plane  of  the  horizon  abcd  :  the  hour  line  upon  the  hori- 
zontal plane  is,  therefore,  a  line  drawn  from  the  centre  of  it,  to 
that  point  where  this  plane  intersects  the  meridian  opposite  to 
that  on  which  the  sun  shines.  Thus,  when  the  sun  is  upon  f,  the 
meridian  of  London,  the  shadow  of  ne  the  axis  will  fall  upon  e, 
XII.  By  the  same  method,  the  rest  of  the  hour  lines  are  found, 
by  drawing,  for  every  hour  a  line  from  the  centre  of  the  horizon- 
tal plane  to  that  meridian,  which  is  diametrically  opposite  to  the 
meridian  pointing  exactly  to  the  sun.  If,  when  the  hour  circles 
are  thus  found,  all  the  lines  be  taken  away  except  the  semi-axis 
NE,  what  remains  will  be  a  horizontal  dial  for  the  given  place. 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


263 


From  what  has  been  premised,  the  following  observations  natu- 
rally arise : 

1.  The  gnomon  of  every  sun-dial  must  always  be  parallel  to 
the  axis  of  the  earth,  and  must  point  directly  to  the  two  poles  of 
the  world. 

2.  As  the  whole  earth  is  but  a  point  when  compared  with  the 
heavens,  therefore,  if  a  small  sphere  of  glass  be  placed  on  any 
part  of  the  earth's  surface,  so  that  its  axis  be  parallel  to  the  axis 
of  the  earth,  and  the  sphere  have  such  lines  upon  it,  and  such  a 
plane  within  it  as  above  described  ;  it  will  show  the  hour  of  the 
day  as  truly  as  if  it  were  placed  at  the  centre  of  the  earth,  and 
the  body  of  the  earth  were  as  transparent  as  glass. 

3.  In  every  horizontal  dial  the  angle  which  the  style,  or  gno- 
mon, makes  with  the  horizontal  plane,  must  always  be  equal  to 
the  latitude  of  the  place  for  which  the  dial  is  made. 

Rule  for  performing  the  problem. — Elevate  the  pole  so 
many  degrees  above  the  horizon  as  are  equal  to  the  latitude  of  the 
place  ;  bring  the  point  Aries  to  the  brass  meridian  ;  then,  as  globes 
in  general*  have  meridians  drawn  through  every  15  degrees  of 
longitude,  eastward  and  westward  from  the  point  of  Aries,  observe 
where  these  meridians  intersect  the  horizon,  and  note  the  num- 
ber of  degrees  between  each  of  them  ;  the  arcs  between  the  res- 
pective hours  will  be  equal  to  these  degrees.  The  dial  must  be 
numbered  XII  at  the  brass  meridian,  thence  XI,  X,  IX,  VIII,  VII, 
VI,  V,  IV,  &:c.  towards  the  west,  for  morning  hours  ;  and  I,  II, 
III,  IV,  V,  VI  VII,  VIII,  &:c.  for  evening  hours.  No  more  hour 
lines  need  be  drawn  than  what  will  answer  to  the  sun's  continu- 
ance above  the  horizon  on  the  longest  day  at  the  given  place. 
The  style  or  gnomon  of  the  dial  must  be  fixed  in  the  centre  of  the 
dial-plate,  and  make  an  angle  therewith  equal  to  the  latitude  of 
the  place.  The  face  of  the  dial  may  be  of  any  shape,  as  round, 
elliptical,  square,  oblong,  &c.  &c. 

Example.  To  make  a  horizontal  dial  for  the  latitude  of  Lon- 
don. 

Having  elevated  the  pole  51  ^  degrees  above  the  horizon,  and  brought  the  point 
Aries  to  the  brass  meridian,  you  will  find  the  meridians  on  the  eastern  part  of  the 
horizon,  reckoning  from  12,  to  be  11"  50',  24°  20',  SS^'  3',  53°  35',  71°  6',  and  90°, 
for  the  hours  I,  II,  III,  IV,  V,  and  VI ;  or,  if  you  count  from  the  east  towards  the 


*  On  Gary's  large  globes,  the  meridians  are  drawn  through  every  ten  degrees,  an 
alteration  which  answers  no  useful  purpose  whatever,  and  is  in  many  cases  very 
inconvenient.  To  solve  this  problem,  by  these  globes,  meridiana  must  be  drawn 
through  every  fifteen  degrees  with  a  pencil. 


264 


PIlOBLEPd:S  PERFORMED  BY 


Part  III. 


eouth,  they  will  be  0°,  18°  54',  36°  25',  51^  57',  65°  40',  and  78^  10',  for  the  hours 
VI,  V,  IV,  III,  II,  I,  reckoning  from  VI  o'clock  backward  to  XII.  There  is  no 
occasion  to  give  the  distances  farther  than  VI,  because  the  distances  from  XII  to 
VI  in  the  forenoon  are  exactly  the  same  as  from  XII  to  VI  in  the  afternoon  ;  and 
hour  lines  continued  through  the  centre  of  the  dial  are  the  hours  on  the  opposite 
parts  thereof 

The  following  Table,  calculated  by  spherical  trigonometry,  contains  not  only 
the  hour  arcs,  but  the  halves  and  quarters  from  XII  to  VI. 


Hours. 

Hour 
Angles. 

Hour 
Arcs. 

Hours. 

Hour 
Angles. 

Hour 
Arcs, 

XII 

0° 

0' 

0 

0' 

34 

48' 

45' 

41'  45' 

m 

3 

45 

2 

56 

3i 

52 

30 

45  34 

7 

30 

5 

52 

3| 

56 

15 

49  30 

12| 

11 

15 

8 

51 

IV 

60 

0 

53  35 

I 

15 

0 

11 

50 

44 
4i 

63 

45 

57  47 

u 

18 

45 

14 

52 

67 

30 

62  6 

22 

30 

17 

57 

4| 

71 

15 

67  33 

ll 

26 

15 

21 

6 

V 

75 

0 

71  6 

II 

30 

0 

24 

20 

54 
54 

78 

45 

75  45 

33 

45 

27 

36 

82 

30 

80  25 

37 

30 

31 

0 

5| 

86 

15 

85  13 

41 

15 

34 

28 

VI 

90 

0 

90  0 

HI 

45 

0 

38 

3 

The  calculation  of  the  hour  arcs  by  spherical  trigonometry  is  extremely  easy  ; 
for  while  the  globe  remains  in  the  position  above  described,  it  will  be  seen  that  a 
right  angled  spherical  triangle  is  formed,  the  perpendicular  of  which  is  the  latitude, 
its  base  the  hour  arc,  and  its  verticl  angle  the  hour  angle.  Hence, 

Radius,  sine  of  90  ' 

Is  to  sine  of  the  latitude  ; 

As  tangent  of  the  hour  angle, 

Is  to  the  tangent  of  the  hour  arc  on  the  horizon. 
It  may  be  observed  here,  that  if  a  horizontal  dial,  which  shows  the  hour  by  the  top 
of  the  perpendicular  gnomon,  be  made  for  a  place  in  the  torrid  zone,  whenever  the 
sun's  declination  exceeds  the  latitude  of  the  place,  the  shadow  of  the  gnomon  will 
go  lack  twice  in  the  day,  once  in  the  forenoon  and  once  in  the  afternoon  ;  and  the 
greater  the  difference  between  the  latitude  and  the  sun's  declination  is,  the  farther 
the  shadow  will  go  back.  In  the  38th  chapter  of  Isiah,  Hezekiah  is  promised  that 
his  life  shall  be  prolonged  15  years,  and  as  a  sign  of  this,  he  is  also  promised  that  the 
shadow  of  the  sun-dial  of  Maz  shall  go  back  ten  degrees.  This  was  truly,  as  it 
was  then  considered  a  miracle;  for,  as  Jerusalem,  the  place  where  the  dial  of  Jlhaz 
was  erected,  was  out  of  the  torrid  zone,  the  shadow  could  not  possibly  go  back 
from  any  natural  cause. 


PROBLEM  LXIV. 

To  make  a  vertical  dial  facing  the  south,  in  north  latitude. 


Definitions  and  Observations. — The  horizontal  dial,  as 
described  in  the  preceding  problem,  was  supposed  to  be  placed 


Chap.  I. 


THE  TERRESTRIAL  GLOBE. 


265 


upon  a  pedestal,  and  as  the  sun  always  shines  upon  such  a  dial  when 
he  is  above  the  horizon,  provided  no  objects  intervene,  it  is  the 
most  complete  of  all  kinds  of  dials.  The  next  in  utility  is  the 
vertical  dial  facing  the  south  in  north  latitudes ;  that  is,  a  dial 
standing  against  the  wall  of  a  building  which  exactly  faces  the 
south. 

Supposing  the  globe  to  be  transparent,  as  in  the  foregoing  prob- 
lem {see  Fig.  5.  Plate  II.)  with  the  hour  circles  or  meridians  f,  g, 
H,  I,  K,  L,  M,  o,  &c.  drawn  upon  it ;  abcd  an  opaque  vertical  plane 
perpendicular  to  the  horizon,  and  passing  through  the  centre  of 
the  globe.  While  the  globe  revolves  round  its  axis  ns,  it  is  evi- 
dent that,  if  the  semi-axis  es  be  opaque  and  cast  a  shadow,  this 
shadow  will  always  fall  upon  the  plane  abc,  and  mark  out  the 
hours  as  in  the  preceding  problem.  By  comparing  Fig.  5.  with 
Fig.  4.  in  Plate  II.  it  will  appear  that  the  plane  surface  of  every 
dial  whatever,  is  parallel  to  the  horizon  of  some  place  or  other 
upon  the  earth,  and  that  the  elevation  of  the  style  or  gnomon 
above  the  dial's  surface,  when  it  faces  the  south,  is  always  equal 
to  the  latitude  of  the  place  whose  horizon  is  parallel  to  that  sur- 
face. Thus  it  appears  that  sp,  which  is  the  co-latitude  of  Lon- 
don, is  the  latitude  of  the  place  whose  horizon  is  represented  by 
the  plane  adcb  :  for,  let  the  south  pole  of  the  globe  be  elevated 
38|^  degrees  above  the  southern  point  of  the  horizon,  and  the 
point  Aries  be  brought  to  the  brass  meridian ;  then,  if  the  globe 
be  placed  upon  a  table,  so  as  to  rest  on  the  south  point  of  the 
wooden  horizon,  it  will  have  exactly  the  appearance  of  Fig.  5. 
Plate  II. ;  the  wooden  horizon,  will  represent  the  opaque  plane 
abcd,  the  south  point  will  be  at  b,  and  the  north  point  at  d  under 
London,  the  east  point  at  c,  and  the  west  point  at  a.  Hence  we 
have  the  following 

Rule  for  performing  the  problem. — If  the  place  be  in 
north  latitude,  elevate  the  south  pole  to  the  complement  of  that 
latitude  ;  bring  the  point  Aries  to  the  brass  meridian ;  then  sup- 
posing meridians  to  be  drawn  through  every  fifteen  degrees  of 
longitude,  eastward  and  westward  from  the  point  Aries  (as  is  gen- 
erally the  case) ;  observe  where  these  meridians  intersect  the 
horizon,  and  note  the  number  of  degrees  between  each  of  them ; 
the  arcs  between  the  respective  hours  will  be  equal  to  these  de- 
grees. The  dial  must  be  numbered  XII,  at  the  brass  meridian, 
thence  XI,  X,  IX,  VIII,  VII,  VI,  towards  the  west,  for  morning 
hours ;  and  I,  II,  III,  IV,  V,  VI,  towards  the  east,  for  evening 
hours.  As  the  sun  cannot  shine  longer  upon  such  a  dial  as  this 
than  from  VI  in  the  morning  to  VI  in  the  evening,  the  hour  lines 
need  not  be  extended  anv  farther. 

34 


266 


PROBLEMS  PERFORMED  BY 


Part  III. 


Example.  To  make  a  vertical  dial  for  the  latitude  of  Lon- 
don. 

Elevate  the  south  pole  38^1  degrees  above  the  horizon,  and  bring  the  point  Aries 
to  the  brass  meridian;  then  the  meridians  will  intersect  the  horizon,  reckoning 
from  the  south  towards  the  east,  in  the  following  degrees ;  9°  28',  19°  45'  31o  54' 
47°  9',  66°  42',  and  90',  for  the  hours  I,  II,  III,  IV,  V,  VI ;  or  if  you  count  from  the 
east  towards  the  south,  they  will  be  0',  23'  18',  42°  51',  58^  6',  70°  15',  80^  42',  for 
the  hours  VI,  V,  IV,  III,  II,  1.  The  distances  from  XII  to  VI  in  the  forenoon  are 
exactly  the  same  as  the  distances  from  XII  to  VI  in  the  afternoon. 

The  following  table  contains  not  only  the  hour  arcs,  but  the  halves  and  quarters 
from  XII  to  VI ;  it  is  calculated  exactly  in  the  same  manner  as  the  table  in  the 
preceding  problem,  using  the  complement  of  the  latitude  instead  of  the  latitude. 


Hours. 

Hour 
Angles. 

Hour 
Arcs. 

Hours, 

Hour 
Angles 

Hour 
Arcs. 

XII 

0 

o  0' 

0° 

0' 

H 

48° 

45' 

35°  22' 

3 

45 

2 

20 

H 

52 

30 

39  3 

7 

30 

4 

41 

3| 

56 

15 

42  58 

12| 

11 

15 

7 

3 

IV 

60 

0 

47  9 

I 

15 

0 

9 

23 

4| 

63 

45 

51  36 

H 

18 

45 

11 

56 

4^ 

67 

30 

56  20 

n 

22 

30 

14 

27 

43. 

71 

15 

61  23 

26 

15 

17 

4 

V  ^ 

75 

0 

66  43 

30 

0 

19 

45 

5h 

78 

44 

72  17 

33 

45 

22 

35 

82 

30 

78  3 

37 

30 

25 

32 

5| 

86 

15 

84  0 

2| 

41 

15 

28 

38 

VI 

90 

0 

90  0 

III 

45 

0 

31 

54 

The  student  will  recollect  that  the  time  shown  by  a  sun-dial  is  not  the  exact  time 
of  the  day,  as  shown  by  a  watch  or  clock  (see  Definitions  55,  56,  and  57,  page  35.) 
A  good  clock  measures  time  equeally,  but  a  sun-dial  (though  used  for  regulating 
clocks  and  watches)  me«,sures  time  unequally.  The  following  table  will  show  to 
the  nearest  minute  how  much  a  clock  should  be  faster  or  slower  than  a  sun-dial ; 
such  a  table  should  be  put  upon  every  horizontal  sun-dial. 


Chap,  I. 


THE  TERRESTRIAL  GLOBE. 


267 


■^3 

m 

n3  . 

S 

CO  ^ 

a> 

3 

a 

3 
C 

Days 
Mont: 

"3 
G 

o 

c 

% 

% 

ps 

Jan.  1 

4 

April  1 

40 

Aug.  9 

5 

4  o" 

Oct.  27 

16 

3 

5 

4 

31" 

15 

Nov.  15 

15 

5 

6 

7 

2^ 

20 

3S- 

20 

14 

7 

7 

11 

IP' 

24 

2 

24 

3  2 

Q 

8 

15 

OS" 

28 

1  ^ 

27 

12 

12 

9 

31 

0? 

30 

11  a, 

15 

10  o 

* 

+ 

Dec  2 

102 

18 

11  9^ 

19 

1 

Sept.  3 

1 

5 

gl 

21 

24 

20 

6 

o 

/ 

8 

25 

13  M 

30 

3  S" 

9 

3^ 

9 

7 

31 

14  CD 

May  13 

4?r 

12 

4  2- 

J 1 

6  ° 

Feb.  10 
21 

15- 
cr 

14  P 

June  5 

3^ 
2| 

15 
18 

5  M 

6o 
7| 

13 
16 

5  3- 
Is 

"-'  P 

27 

13^ 

10 

1? 

21 

18 

Mar.  4 

12  ^ 

15 

0 

24 

8  ^ 

20 

2  •'^ 

8 

Hid 

* 

27 

9p 

22 

1 

12 

10 

20 

1  o 

30 

10^ 

24 

0 

15 

9' 

25 

2° 

Oct.  3 

+ 

19 
22 

8 
7 

29 

July  5 

3=^ 
45^ 

6 
10 

12  Q 
13^- 

26 
28 

25 

6 

11 

5^ 

14 

30 

3s. 

28 

5 

28 

6^ 

19 

15 

CD 

Dials  may  be  constructed  on  all  kinds  of  planes,  whether  horizontal  or  inclined  ; 
a  vertical  dial  may  be  made  to  face  the  south,  or  any  point  of  the  compass  ;  but 
the  two  dials  already  described  are  the  most  useful.  To  acquire  a  complete  knowl- 
edge of  dialling,  the  gnomonical  projection  of  the  sphere,  and  the  principles  of 
spherical  trigonometry,  must  be  thoroughly  understood  ;  these  preliminary  branches 
may  be  learned  from  Emerson's  Gnomonical  Projection,  and  Keith^s  Trigonometry. 
The  writers  on  dialling  are  very  numerous  ;  the  last  and  best  treatise  on  the  sub- 
ject is  Emerson's. 


^68 


PROBLEMS  PERFORMED  BY 


Part  111. 


CHAPTER  II. 

Problems  performed  by  the  Celestial  Globe. 
PROBLEM  LXV. 


To  find  the  right  ascension  and  declination  of  the  sun*,  or  a  star. 

Rule.  Bring  the  sun  or  star  to  that  part  of  the  brass  meridian 
which  is  numbered  from  the  equinoctial  towards  the  poles  ;  the 
degree  on  the  brass  meridian  is  the  declination,  and  the  number 
of  degrees  on  the  equinoctial,  between  the  brass  meridian  and  the 
point  Aries,  is  the  right  ascension. 

Or,  Place  both  the  poles  of  the  globe  in  the  horizon,  bring  the 
sun  or  star  to  the  eastern  part  of  the  horizon ;  then  the  number  of 
degrees  which  the  sun  or  star  is  northward  or  southward  of  the 
east,  will  be  the  declination  north  or  south ;  and  the  degrees  on  the 
equinoctial,  from  Aries  to  the  horizon,  will  be  the  right  ascension. 

Examples.  I.  Required  the  right  ascension  and  dechnation 
of  a  Dubhe,  in  the  back  of  the  Great  Bear. 

Answer.    Right  ascension  162°  49',  declination  62°  48'  N. 

2.  Required  the  right  ascensions  and  declinations  of  the  fol- 
lowing stars : 

i3,  Rigel,  in  Orion, 
y,  Bellatrix,  in  Orion. 
a,  Betelgeux,  in  Orion, 
a,  Canopus,  in  Argo  Navis. 
a,  Procyon,  in  the  Little  Dog. 
y,  Algorab,  in  the  Crow. 
a,  Arcturus,  in  Bootes, 
e,  Vendemiatrix,  in  Virgo. 


Algenib,  in  Pegasus. 
a,  Scheder,  in  Cassiopeia. 
/3,  Mirach,  in  Andromeda. 
a,  Acherner,  in  Eridanus. 
«,  Menkar,  in  Cetus. 
/3,  Algol,  in  Perseus. 
a,  Aldebaran,  in  Taurus. 
a,  Capella,  in  Auriga. 


*  The  right  ascensions  and  declinations  of  the  moon  and  planets  must  be  found 
from  an  ephemeris  ;  because,  by  their  continual  change  of  situation,  they  cannot 
be  placed  on  the  celestial  globe,  as  the  stars  are  placed. 


Chap,  II. 


THE  CELESTIAL  GLOBE. 


269 


PROBLEM  LXVI. 


To  find  the  latitude  and  longitude  of  a  star.* 

Rule.  Place  the  upper  end  of  the  quadrant  of  altitude  on  the 
north  or  south  pole  of  the  ecliptic,  according  as  the  star  is  on  the 
north  or  south  side  of  the  ecliptic,  and  move  the  other  end  till  the 
star  conies  to  the  graduated  edge  of  the  quadrant ;  the  number  of 
degrees  between  the  ecliptic  and  the  star  is  the  latitude  ;  and  the 
number  of  degrees  on  the  ecliptic,  reckoned  eastward  from  the 
point  Aries  to  the  quadrant,  is  the  longitude. 

Or,  Elevate  the  north  or  south  pole  66|  °  above  the  horizon ; 
according  as  the  given  star  is  on  the  north  or  south  side  of  the 
ecliptic  ;  bring  the  pole  of  the  ecliptic  to  that  part  of  the  brass 
meridian  which  is  numbered  from  the  equinoctial  towards  the 
pole  ;  then  the  ecliptic  will  coincide  with  the  horizon ;  screw  the 
quadrant  of  altitude  upon  the  brass  meridian  over  the  pole  of  the 
ecliptic  ;  keep  the  globe  from  revolving  on  its  axis,  and  move  the 
quadrant  till  its  graduated  edge  comes  over  the  given  star ;  the 
degree  on  the  quadrant  cut  by  the  star  is  its  latitude  ;  and  the  sign 
and  degree  on  the  ecliptic  cut  by  the  quadrant  show  its  longitude. 

Examples.  1.  Required  the  latitude  and  longitude  of  a 
Aldeharan  in  Taurus. 

Answer.    Latitude  5«>  28'  S.,  longitude  2  signs  6°  53' ;  or  6«  53'  in  Gemini. 

2.  Required  the  latitudes  and  longitudes  of  the  following  stars. 


fl,  Markab,  in  Pegasus. 
/5,  Scheat,  in  Pegasus, 
a,  Fomalhaut,  in  the  S.  Fish, 
a,  Deneh,  in  Cygnus. 
a,  Altair,  in  the  Eagle. 
Alhireo,  in  Cygnus. 


Vega,  in  Lyra. 
Rastaben,  in  Draco. 
Antares,  in  the  Scorpion. 
Arcturus,  in  Bootes. 
Pollux,  in  Gemini. 
Rigel,  in  Orion. 


*  Tha  latitudes  and  longitudes  of  the  planets  must  be  found  from  an  ephemeris. 


270 


PROBLEMS  PERFORMED  BY 


Part  III. 


PROBLEM  LXVII. 

The  right  ascension  and  declination  of  a  star,  the  moon,  a  planet, 
or  of  a  comet,  being  given,  to  find  its  place  on  the  globe. 

Rule.  Bring  the  given  degrees  of  right  ascension  to  that  part 
of  the  brass  meridian  which  is  numbered  from  the  equinoctial 
tow^ards  the  poles  ;  then  under  the  given  declination  on  the  brass 
meridian  you  will  find  the  star,  or  place  of  the  planet. 

Examples.  1.  What  star  has  261°  29'  of  right  ascension,  and 
52°  27  north  declination  ? 


Answer. 


/3 


in  Draco. 


2.  On  the  31st  of  January,  1825,  the  moon's  right  ascension 
was  91°  21',  and  her  declination  23°  19'  N. ;  find  her  place  on 
the  globe  at  that  time. 

Answer.  In  the  milky  way,  a  little  above  the  left  foot  of  Castor. 

3.  What  stars  have  the  following  right  ascensions  and  declina- 
tions ? 


Right  Ascensions. 

7°  19' 
11  11 

25  54 
46  32 
53  54 
74  14 


Declinations. 

55°  26'  N. 
59  38 
19  50 

9  34 
23  19 

8  27 


N. 
N. 
S. 
N. 
S. 


Right  Ascensions.  Declinations. 


83° 
86 


6' 
13 
99  5 
110  27 


113 
129 


16 

2 


34°  11/  S. 
44  55  N. 
16  26  S. 
32  19  N. 
28  30  N. 
7    8  N. 


4.  On  the  seventh  of  March,  1826,  the  moon's  right  ascension 
at  midnight  will  be  333°  2',  and  her  declination  5^^  44'  S. ;  find 
her  place  on  the  globe. 

5.  On  the  13th  of  May,  1826,  the  declination  of  Venus  will 
be  22°  ir  N.,  and  her  right  ascension  66^^  45' ;  find  her  place  on 
the  globe  at  that  time. 

6.  On  the  first  of  July,  1826,  the  declination  of  Jupiter  will 
be  9°  4'  N.,  and  his  right  ascension  161°  30' ;  find  his  place  on 
the  globe  at  that  time. 


PROBLEM  LXVIII. 

The  latitude  and  longitude  of  the  moon,  a  star,  or  of  a  planet,  being 
given,  to  find  its  place  on  the  globe. 

Rule.  Place  the  division  of  the  quadrant  of  altitude  marked 
o,  on  the  given  longitude  in  the  ecliptic,  and  the  upper  end  on  the 


Chap.  II. 


THE  CELESTIAL  GLOBE. 


271 


pole  of  the  ecliptic ;  then,  under  the  given  latitude,  on  the  grad- 
uated edge  of  the  quadrant,  you  will  find  the  star,  or  place  of  the 
moon  or  planet. 

Examples.  1.  What  star  has  0  signs  6°  16'  of  longitude,  and 
12°  36'  N.  latitude. 


.Answer,    y  in  Pegasus. 

2.  On  the  15th  of  June  1826,  at  noon,  the  moon^s  longitude 
will  be  6s  22°  24',  and  her  latitude  3°  24'  S. :  find  her  place  on 
the  globe. 

3.  What  stars  have  the  following  latitudes  and  longitudes  ? 


Latitudes. 

12*^  35  S. 
5  29  S. 
31  8  S. 
22  52  N. 
16    3  S. 


Longitudes. 


ir 

6 
13 
18 

25 


25' 
53 
56 
57 
51 


Latitudes. 

39°  33'  S. 
10  4  N. 
0  27  N. 
44  20  N. 
21    6  S. 


Longitudes. 

3s  n  13' 

3  17 

4  26 
7  9 

11  0 


21 

57 
22 
56 


4.  On  the  13th  of  November  1826,  at  noon,  the  longitudes  and 
latitudes  of  the  planets  will  be  as  follow :  required  their  places 
on  the  globe. 

Latitudes. 

%  13'  S. 
4  10  S. 


Longitudes. 

^  8s  8^  11' 
?  5  2  37 
9  25  25 


1  39  S. 


Longitudes. 

U  6s  6°  24' 
^  3  5  33 
JJt  9  20  56 


Latitudes. 

1°  9'N. 
0  59  S. 
0  29  S. 


PROBLEM  LXIX. 


The  day  and  hour,  and  the  latitude  of  a  place  being  given,  to  find 
what  stars  are  rising,  setting,  culminating,  <SfC, 

Rule.  Elevate  the  pole  to  the  latitude  of  the  place,  find  the 
sun's  place  in  the  ecliptic,  bring  it  to  the  brass  meridian,  and  set 
the  index  of  the  hour  circle  to  twelve  ;  then,  if  the  time  be  before 
noon,  turn  the  globe  eastward  on  its  axis  till  the  index  has  passed 
over  as  many  hours  as  the  time  wants  of  noon,  but,  if  the  time 
be  past  noon,  turn  the  globe  westward  till  the  index  has  passed 
over  as  many  hours  as  the  time  is  past  noon :  then  all  the  stars 
on  the  eastern  semi-circle  of  the  horizon  will  be  rising,  those  on 
the  western  semi-circle  will  be  the  setting,  those  under  the  brass 
meridian  above  the  horizon  will  be  the  culminating,  those  above 
the  horizon  will  be  visible  at  the  given  time  and  place,  those  be- 
low will  be  invisible. 


272 


PROBLEMS  PERFORMED  BY 


Part  III. 


If  the  globe  be  turned  on  its  axis  from  east  to  west,  those  stars 
which  do  not  go  below  the  horizon  never  set  at  the  given  place ; 
and  those  which  do  not  come  above  the  horizon  never  rise ;  or,  if 
the  given  latitude  be  subtracted  from  90  degrees,  and  circles  be 
described  on  the  globe,  parallel  to  the  equinoctial,  at  a  distance 
from  it  equal  to  the  degrees  in  the  remainder,  they  will  be  the 
circles  of  perpetual  apparition  and  occultation. 

Examples.  1.  On  the  9th  of  February,  when  it  is  nine  o'clock 
in  the  evening  at  London,  what  stars  are  rising,  what  stars  are 
setting,  and  what  stars  are  on  the  meridian  ? 

Answer.  Alphacca,  in  the  northern  Crown  is  rising;  Arcturus  and  Mirach,  in 
Bootes,  just  above  the  horizon ;  Sirius  on  the  meridian  ;  Procyon  and  Castor  and 
Pollux  a  little  east  of  the  meridian.  The  constellations  Orion,  Taurus,  and  Au- 
riga, a  Uttle  west  of  the  meridian  ;  Markab,  in  Pegasus,  just  below  the  western 
edge  of  the  horizon,  &c. 

2.  On  the  20th  of  January,  at  two  o'clock  in  the  morning  at 
London,  what  stars  are  rising,  what  stars  are  setting,  and  what 
stars  are  on  the  meridian  ? 

Answer.  Vega  in  Lyra,  the  head  of  the  Serpent,  Spica  Virginis,  &.  are  rising ; 
the  head  of  the  Great  Bear,  the  claws  of  Cancer,  &c.  on  the  meridian ;  the  head  of 
Andromeda,  the  neck  of  Cetus,  and  the  body  of  Columba  Noachi,  &c.  are  setting. 

3.  At  ten  o'clock  in  the  evening  at  Edinburgh,  on  the  15th  of 
November,  what  stars  are  rising,  what  stars  are  setting,  and  what 
stars  are  on  the  meridian  ? 

4.  What  stars  do  not  set  in  the  latitude  of  London,  and  at 
what  distance  from  the  equinoctial  is  the  circle  of  perpetual  ap- 
parition ? 

5.  What  stars  do  not  rise  to  the  inhabitants  of  Edinburgh,  and 
at  what  distance  from  the  equinoctial  is  the  circle  of  perpetual 
occultation  ? 

6.  What  stars  never  rise  at  Otaheite,  and  what  stars  never  set 
at  Jamaica  ? 

7.  How  far  must  a  person  travel  southward  from  London  to 
lose  sight  of  the  Great  Bear  ? 

8.  What  stars  are  continually  above  the  horizon  at  the  north 
pole,  and  what  stars  are  constantly  below  the  horizon  thereof? 


/ 


Chap.  IL 


THE   CELESTIAL  GLOBE. 


273 


PROBLEM  LXX. 

The  Latitude  of  a  place,  day  of  the  month,  and  hour  being  given, 
to  place  the  globe  in  such  a  manner  as  to  represent  the  heavens 
at  that  time ;  in  order  to  find  out  the  relative  situations  and 
names  of  the  constellations  and  remarkable  stars. 

Rule.  Take  the  globe  out  into  the  open  air,  on  a  clear  star- 
light night,  where  the  surrounding  horizon  is  uninterrupted  by 
different  objects  ;  elevate  the  pole  to  the  latitude  of  the  place,  and 
set  the  globe  due  north  and  south  by  a  meridian  line,  or  by  a 
mariner's  compass,  taking  care  to  make  a  proper  allowance  for 
the  variation  ;  find  the  sun's  place  in  the  ecliptic,  bring  it  to  the 
brass  meridian  and  set  the  index  of  the  hour-circle  to  twelve ; 
then,  if  the  time  be  after  noon,  turn  the  globe  westward  on  its  axis, 
till  the  index  has  passed  over  as  many  hours  as  the  time  is  past 
noon  ;  but,  if  the  time  be  before  noon,  turn  the  globe  eastward  till 
the  index  has  passed  over  as  many  hours  as  the  time  wants  of 
noon ;  fix  the  globe  in  this  position,  then  the  flat  end  of  a  pencil 
being  placed  on  any  star  on  the  globe  so  as  to  point  towards  the 
centre,  the  other  end  will  point  to  that  particular  star  in  the 
heavens. 


PROBLEM  LXXL 

To  find  when  any  star,  or  planet,  will  rise,  come  to  the  meridiaut 
and  set  at  any  given  place. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place  ;  find  the  sun's  place  in 
the  ecliptic,  bring  it  to  the  brass  meridian,  and  set  the  index  of 
the  hour-circle  to  twelve.  Then  if  the  star*  or  planet  be  below 
the  horizon,  turn  the  globe  westward  till  the  star  or  planet  comes 
to  the  eastern  part  of  the  horizon,  the  hours  passed  over  by  the 
index  will  show  the  time  from  noon  when  it  rises ;  and,  by  con- 
tinuing the  motion  of  the  globe  westward  till  the  star,  &c.  comes 


*  The  latitude  and  longitude  (or  the  right  ascension  and  declination)  of  the 
planet  must  be  taken  from  an  ephemeris,  and  its  place  on  the  globe  must  be 
detiermined  by  Prob.  LXVIII.  (or  LXVII.) 

35 


274 


PROBLEMS  PERFORMED  BY 


Part  IIL 


to  the  meridian,  and  to  the  western  part  of  the  horizon  suc- 
cessively, the  hours  passed  over  by  the  index  will  show  the  time 
of  culminating  and  setting. 

If  the  star,  &c.  be  above  the  horizon  and  east  of  the  meridian, 
find  the  time  of  culminating,  setting,  and  rising,  in  a  similar 
manner.  If  the  star,  &c.  be  above  the  horizon  west  of  the 
meridian,  find  the  time  of  setting,  rising,  and  culminating,  by 
turning  the  globe  westward  on  its  asis. 

Examples.  I.  At  what  time  will  Arcturus  rise,  come  to  the 
meridian,  and  set,  at  London,  on  the  7th  of  September? 

Answer,  It  will  rise  at  seven  o'clock  in  the  morning,  come  to  the  meridian  at 
three  in  the  afternoon,  and  set  at  1 1  o'clock  at  night. 

2.  On  the  first  of  August,  1805,  the  longitude  of  Jupiter  was 
7  signs,  26  degrees,  34  minutes,  and  his  latitude  45  minutes  N. ; 
at  what  time  did  he  rise,  culminate,  and  set,  at  Greenwich,  and 
whether  was  he  a  mornin^i:  or  an  evening  star  ? 

Answer.  Jupiter  rose  at  half-past  two  in  the  afternoon,  came  to  the  meridian  at 
about  ten  minutes  to  seven,  and  set  at  a  quarter  past  eleven  in  the  evening.  Here 
Jupiter  was  an  evening  star,  because  he  set  after  the  sun. 

3.  At  what  time  does  Sirius  rise,  come  to  the  meridian  of 
London,  and  set,  on  the  31st  of  January? 

4.  On  the  first  of  January,  1825,  the  longitude  of  Venus  was 
10  signs  18  deg.  51  min.,  and  her  latitude  1  deg.  48  min.  S.  ;  at 
what  time  did  she  rise,  culminate,  and  set,  at  Paris,  and  whether 
was  she  a  morning  or  an  evening  star  ? 

5.  At  what  time  does  Aldebaran  rise,  come  to  the  meridian, 
and  set  at  Dublin,  on  the  25th  of  November  ? 

6.  On  the  first  of  February,  1825,  the  longitude  of  Mars  was 
eleven  signs  9  deg.  59  min.,  and  latitude  0  deg.  53  min.  S. ; 
at  what  time  did  he  rise  set,  and  come  to  the  meridian  of 
Greenwich  ? 

PROBLEM  LXXII. 

To  find  the  amplitude  of  any  star,  its  oblique  ascension  and 
descension,  and  its  diurnal  arc  for  any  given  day. 

Rule.  Elevate  the  pole  to  the  latitude  of  the  place,  and  bring  the 
given  star  to  the  eastern  part  of  the  horizon ;  then  the  number 
of  degrees  between  the  star  and  the  eastern  point  of  the  horizon 
will  be  its  rising  amplitude;  and  the  degree  of  the  equinoctial 
cut  by  the  horizon  will  be  the  oblique  ascension ;  set  the  index 


ehap,  II. 


THE   CELESTIAL  GLOBE. 


275 


of  the  hour-circle  to  twelve,  and  turn  the  globe  westward  till 
the  given  star  comes  to  the  western  egde  of  the  horizon ;  the 
hours  passed  over  by  the  index  will  be  the  star's  diurnal  arc,  or 
continuance  above  the  horizon.  The  setting  amplitude  will  be 
the  number  of  degrees  between  the  star  and  the  western  point  of 
the  horizon,  and  the  oblique  descension  will  be  represented  by 
that  degree  of  the  equinoctial  which  is  intersected  by  the  hor- 
izon, reckoning  from  the  point  Aries. 

Examples.  I.  Required  the  rising  and  setting  amplitude  of 
Sirius,  its  oblique  ascension,  oblique  descension,  and  diurnal  arc, 
at  London. 

Answer.  The  rising  amplitude  is  27°  to  the  south  of  the  cast ;  setting  amplitude 
ST-' south  of  the  west ;  oblique  ascension  120  -;  oblique  descension  77° ;  and  di- 
urnal arc  9  hours  6  minutes. 

2.  Required  the  rising  and  setting  amplitude  of  Aldebaran,  its 
oblique  ascension,  oblique  descension,  and  diurnal  arc,  at  Lon- 
don. 

3.  Required  the  rising  and  setting  amplitude  of  Arcturus,  its 
oblique  ascension,  oblique  descension,  and  diurnal  arc,  at  Lon- 
don. 

4.  Required  the  rising  and  setting  amplitude  of  y  Bellatrix, 
its  oblique  ascension,  oblique  descension,  and  diurnal  arc,  at  Lon- 
don. 


PRtBLEM  LXXIII. 

The  latitude  of  a  "place  given,  to  find  the  time  of  the  year  at  which 
any  known  star  rises  or  sets  acronically,  that  is,  when  it  rises 
or  sets  at  sun-setting. 

Rule.  Elevate  the  pole  to  the  latitude  of  the  place,  bring  the 
given  star  to  the  eastern  edge  of  the  horizon,  and  observe  what 
degree  of  the  ecliptic  is  intersected  by  the  western  edge  of  the 
horizon,  the  day  of  the  month  answering  to  that  degree  will  show 
the  time  when  the  star  rises  at  sun-set,  and  consequently  when  it 
begins  to  be  visible  in  the  evening.  Turn  the  globe  westward  on 
its  axis  till  the  star  comes  to  the  western  edge  of  the  horizon,  and 
observe  what  degree  of  the  ecliptic  is  intersected  by  the  horizon 
as  before :  the  day  of  the  month  answering  to  that  degree  will 
show  the  time  when  the  star  sets  with  the  sun,  or  when  it  ceases 
to  appear  in  the  evening. 

Examples.   1.  At  what  time  does  Arcturus  rise  acronically  at 


276 


PROBLEMS  PERFORMED  BY 


Part  III. 


Ascra^  in  Boeotia,  the  birth-place  of  Hesiod  ;  the  latitude  of 
Ascra,  according  to  Ptolemy,  being  37°  45  N.  ? 

Answer,  When  Arcturus  is  at  the  eastern  part  of  the  horizon,  the  eleventh 
degree  of  Aries  will  be  at  the  western  part  answering  to  the  first  of  April,!  the 
time  when  Arcturus  rises  acronically :  and  it  will  set  acronically  on  the  30th  of 
November. 

2.  At  what  time  of  the  year  does  Aldebaran  rise  acronically 
at  Athens,  in  38°  N.  latitude';  and  at  what  time  of  the  year  does 
it  set  acronically  ? 

3.  On  what  day  of  the  year  does  y  in  the  extremity  of  the  wing 
of  Pegasus  rise  acronically  at  London ;  and  on  what  day  of  the 
year  does  it  set  acronically  ? 

4.  On  what  day  of  the  year  does  e  in  the  right  foot  of  Lepus 
rise  acronically  at  London  ;  and  on  what  day  of  the  year  does  it 
set  acronically  ? 


PROBLEM  LXXIV. 


The  latitude  of  a  place  given,  to  find  the  time  of  the  year  at  which 
any  known  star  rises  or  sets  cosmically,  that  is,  when  it  rises 
or  sets  at  sun-rising. 

Rule.  Elevate  the  pole  to  the  latitude  of  the  place,  bring  the 
given  star  to  the  eastern  edge  of  the  horizon,  and  observe  what 
sign  and  degree  of  the  ecliptic  are  intersected  by  the  horizon  ; 
the  month  and  day  of  the  month,  answering  to  that  sign  and  de- 
gree, will  show  the  time  when  the  star  rises  with  the  sun.  Turn 
the  globe  westward  on  its  axis  till  the  star  comes  to  the  western 


*  See  page  37. 

f  Hence  Arcturus  now  rises  acronically  in  latitude  37°  45'  N.  about  100  days 
after  the  winter  solstice.    Hesiod,  in  his  Opera  and  Dies  hb.  ii.  verse  185,  says  : 

When  from  the  solstice  sixty  wintry  days 

Their  turns  have  finished,  mark,  with  glitt'ring  rays, 

From  Ocean's  sacred  flood  Arcturus  rise. 

Then  first  to  gild  the  dusky  evening  skies. 
Here  is  a  difference  of  40  days  in  the  acronical  rising  of  this  star  (supposing  He- 
siod to  be  correct)  between  the  time  of  Hesiod  and  the  present  time  ;  and  as  a  day 
answers  to  about  59'  of  the  echptic  (see  the  note  page  36,)  40  days  will  answer  to 
39  degrees  ;  consequently,  the  winter  solstice  in  the  lime  of  Hesiod  was  in  the  9th 
degree  of  Aquarius.  Now,  the  recession  of  the  equinoxes  is  about  50|"  in  a  year: 
hence  50^''  :  1  year  :  :  39°  :  2794  years  since  the  time  of  Hesiod  ;  so  that  he  lived 
990  years  before  Christ,  by  this  mode  of  reckoning.  Lempriere,  in  his  Classical 
Dictionary,  says  Hesiod  lived  90,7  years  before  Christ. 


Chap.  II. 


THE  CELESTIAL  GLOBE. 


277 


edge  of  the  horizon,  and  observe  what  sign  and  degree  of  the  eclip- 
tic are  intersected  by  the  eastern  edge,  as  before  ;  these  will  point 
out  on  the  horizon  the  time  when  the  star  sets  at  sun-rising. 

Examples.  1.  At  what  time  of  the  year  do  the  Pleiades  set 
cosmically  at  Miletus  in  Ionia,  the  birth-place  of  Thales  ;  and  at 
what  time  of  the  year  do  they  rise  cosmically ;  the  latitude  of 
Miletus,  according  to  Ptolemy,  being  37°  north? 

Answer.  The  Pleiades  rise  with  the  sun  on  the  lOth  of  May,  and  they  set  at  the 
time  of  sun- rising  on  the  22d  of  November.* 

2.  At  what  time  of  the  year  does  Sirius  rise  with  the  sun  at 
London  ;  and  at  what  time  of  the  year  will  Sirius  set  when  the 
sun  rises  ? 

3.  At  what  time  of  the  year  does  Menkar,  in  the  jav^r  of  Cetus, 
rise  with  the  sun,  and  at  what  time  does  it  set  at  sun-rising  at 
London  ? 

4.  At  what  time  of  the  year  does  Procyon,  in  the  Little  Dog, 
set  when  the  sun  rises  at  London,  and  at  what  time  of  the  year 
does  it  rise  with  the  sun  ? 


PROBLEM  LXXV. 

To  find  the  time  of  the  year  when  any  given  star  rises  or  sets 

HELICALLY,  "t" 

Rule.  The  heliacal  rising  and  setting  of  the  stars  will  vary 
according  to  their  different  degrees  of  magnitude  and  brilliancy  ; 
for  it  is  evident  that  the  brighter  a  star  is  when  above  the  horizon. 


*  PUny  says  (Nat.  Hist.  Hb.  xviii.  cap.  25.)  that  Thales  determined  the  cosmical 
setting  of  the  Pleiades  to  be  twenty-five  days  after  the  autumnal  equinox.  Sup- 
posing this  observation  to  be  made  at  Miletus,  there  will  be  a  diflTerence  of  thirty- 
five  days  in  the  cosmical  setting  of  this  star  since  the  time  of  Thales ;  and,  as  a 
day  answers  to  about  59'  of  the  ecliptic,  these  days  will  make  about  34  25'  ;  con- 
sequently, in  the  time  of  Thales,  the  autumnal  equinoctial  colure  passed  through 
4°  25'  of  Scorpio  ;  and,  as  before,  bO^''  :  1  year  :  :  34°  25' :  2465  years  since  the 
time  of  Thales,  so  that  Thales  lived  (2465—1804)  661  years  before  the  birth  of 
Christ.  According  to  Sir.  I.  Newton's  Chronology,  Thales  flourished  596  years 
before  Christ.  Thales  was  well  skilled  in  geometry,  astronomy,  and  philosophy ; 
he  measured  the  height  and  extent  of  the  Pyramids  of  Egypt,  was  the  first  who 
calculated  with  accuracy  a  solar  eclipse  ;  he  discovered  the  solstices  and  equinoxes, 
divided  the  heavens  into  five  zones,  and  recommended  the  division  of  the  year  into 
365  days.  Miletus  was  situated  in  Asia  Minor,  south  of  Ephesus,  and  south-east 
of  the  island  of  Samos. 

t  See  Definition  90.,  page  45. 


278 


PROBLEMS  PERFORMED  BY 


Part  III. 


the  less  the  sun  will  be  depressed  below  the  horizon  w^hen  that 
star  first  becomes  visible.  According  to  Ptolemy,  stars  of  the 
first  magnitude  are  seen  rising  and  setting  when  the  sun  is  twelve 
degrees  below  the  horizon  ;  stars  of  the  second  magnitude  require 
the  sun's  depression  to  be  thirteen  degrees ;  stars  of  the  third 
magnitude  fourteen  degrees,  and  so  on,  reckoning  one  degree  for 
each  magnitude.    This  being  premised  : 

To  SOLVE  THE  PROBLEM.  Elcvatc  the  pole  so  many  degrees 
above  the  horizon  as  are  equal  to  the  latitude  of  the  place,  and 
screw  the  quadrant  of  altitude  on  the  brass  meridian  over  that 
latitude  ;  bring  the  given  star  to  the  eastern  edge  of  the  horizon, 
and  move  the  quadrant  of  altitude  till  it  intersects  the  ecliptic 
twelve  degrees  below  the  horizon,  if  the  star  be  of  the  first  mag- 
nitude ;  thirteen  degrees,  if  the  star  be  of  the  second  magnitude  ; 
fourteen  degrees,  if  it  be  of  the  third  magnitude,  &c. :  the  point 
of  the  ecliptic,  cut  by  the  quadrant,  will  show  the  day  of  the 
month,  on  the  horizon,  when  the  star  rises  heliacally.  Bring  the 
given  star  to  the  western  edge  of  the  horizon,  and  move  the 
quadrant  of  altitude  till  it  intersects  the  ecliptic  below  the  west- 
ern edge  of  the  horizon,  in  a  similar  manner  as  before  ;  the  point 
of  the  ecliptic  cut  by  the  quadrant  will  show  the  day  of  the  month, 
on  the  horizon,  when  the  star  sets  heliacally. 

Examples.  1.  At  what  time  does  /3  Tauri,  or  the  bright  star 
in  the  Bull's  Horn,  of  the  second  magnitude,  rise  and  set  helia- 
cally at  Rome  ? 

Answer.  The  quadrant  will  intersect  the  third  of  Cancer  IS*'  below  the  eastern 
horizon,  answering  to  the  24th  of  June;  and  the  7th  of  Gemini  13°  below  the 
western  horizon,  answering  to  the  28th  of  May. 

2.  At  what  time  of  the  year  does  Sirius,  or  the  Dog  Star,  rise 
heliacally  at  Alexandria  in  Egypt ;  and  at  what  time  does  it  set 
heliacally  at  Alexandria  in  Egypt ;  and  at  what  time  does  it  set 
heliacally  at  the  same  place  ? 

Answer.  The  latitude  of  Alexandria  is  31  deg.  13  min.  north  ;  the  quadrant  will 
intersect  the  12th  of  Leo,  12^  below  the  eastern  horizon,  answering  to  the  4th  of 
August*  ;  and  the  2d  of  Gemini,  12  degrees  below  the  western  horizon,  answering 
to  the  23d  of  May. 


*  The  ancients  reckoned  the  beginning  of  the  Dog  Days  from  the  heliacal  rising 
of  Sirius,  and  their  continuance  to  be  about  40  days.  Hesiod  informs  us  that  the 
hottest  season  of  the  year  (Dog  Days)  ended  about  50  days  after  the  summer  sol- 
stice. We  have  determined  in  the  note  of  Example  1.  Problem  LXXIII.  (though 
perhaps  not  very  accurately),  that  the  winter  solstice,  in  the  time  of  Hesiod,  was 
in  the  9th  degree  of  Aquarius  ,•  consequently,  the  summer  solstice  was  in  the  9th 
degree  of  Leo :  now,  it  appears  from  above,  that  Sirius  rises  hehacally  at  Alex- 
andria when  the  sun  is  in  the  12th  degree  of  Leo  ;  and,  as  a  degree  nearly  answers 
to  a  day,  Sirius  rose  heliacally  in  the  time  of  Hesiod,  about  four  days  after  the 


Chap,  11. 


THE   CELESTIAL  GLOBE. 


279 


3.  At  what  time  of  the  year  does  Arcturus  rise  heliacally  at 
Jerusalem,  and  at  what  time  does  it  set  heliacally  ? 

4.  At  what  time  of  the  year  does  Cor  Hydra3  rise  and  set  heli- 
acally at  London  ? 

5.  At  what  time  of  the  year  does  Procyon  rise  and  set  heli- 
acally at  London? 

6.  If  the  precession  of  the  equinoxes  be  50^  seconds  in  a  year, 
how  many  years  will  elapse,  from  1825  before  Sirius,  the  Dog 
Star,  will  rise  heliacally  at  Christmas,  at  Cairo  in  Egypt?  When 
this  period  happens,  Sirius  will  perhaps  no  longer  be  accused  of 
bringing  sultry  weather. 


PROBLEM  LXXVL 

The  latitude  of  a  place  and  day  of  the  month  being  given,  to  find 
all  those  stars  that  rise  and  set  acronically,  cosmically,  and 

HELIACALLY.* 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  given  place.  Then, 

L  For  the  acronical  rising  and  setting,  find  the  sun's  place  in 
the  ecliptic,  and  bring  it  to  the  western  edge  of  the  horizon,  and 


summer  solstice ;  and  if  the  Dog  Days  continued  forty  days,  they  ended  about 
forty-four  days  after  the  summer  solstice.  The  Dog  Days  in  our  almanacs  begin 
on  the  third  of  July,  which  is  twelve  days  after  the  summer  solstice,  and  end  on 
the  11th  of  August,  which  is  fifty-one  days  after  the  summer  solstice;  and  their 
continuance  is  39  days.  Hence  it  is  plain,  that  the  Dog  Days  of  the  moderns  have 
no  reference  whatever  to  the  rising  of  Sirius,  for  this  star  rises  heliacally  at  London 
on  the  25th  of  August,  and,  as  well  as  the  rest  of  the  stars,  varies  in  its  rising  and 
setting  according  to  the  variation  of  the  latitudes  of  places,  and  therefore  it  could 
have  no  influence  whatever  on  the  temperature  of  the  atmosphere  ;  yet,  as  the  Dog 
Star  rose  heliacally  at  the  commencement  of  the  hottest  season  in  Egypt,  Greece, 
&c.  in  the  earUer  ages  of  the  world,  it  was  very  natural  for  the  ancients  to  imagine 
that  the  heat,  &c.  was  the  effect  of  this  star.  A  few  years  ago,  the  Dog  Days  in 
our  almanacs  began  at  the  cosmical  rising  of  Procyon,  viz.  on  the  30ih  of  July,  and 
continued  to  the  7th  of  September  ;  but  they  are  now,  very  properly,  altered,  and 
made  not  to  depend  on  the  variable  rising  of  any  particular  star,  but  on  the  sum- 
mer solstice. 

*  This  problem  is  the  reverse  of  the  three  preceding  problems.  Their  principal 
use  is  to  illustrate  several  passages  in  the  ancient  writers,  such  as  Hesiod,  Virgil, 
Columella,  Ovid,  Phny,  &c.  See  definition  64.,  page  37.  The  knowledge  of  these 
poetical  risings  and  settings  of  the  stars  was  held  in  great  esteem  among  the  an- 
cients, and  was  very  useful  to  them  in  adjusting  the  times  set  apart  for  their  reli- 
gious and  civil  duties,  and  for  marking  the  seasons  proper  for  the  several  parts  of 


280 


PROBLEMS  PERFORMED  BY 


Part  III. 


all  the  stars  along  the  eastern  edge  of  the  horizon  will  rise  acron- 
ically,  while  those  along  the  western  edge  will  set  acronically. 

2.  For  the  cosmical  rising  and  setting,  bring  the  sun's  place  to 
the  eastern  edge  of  the  horizon,  and  all  the  stars  along  that  edge 
of  the  horizon  will  rise  cosmically,  while  those  along  the  western 
edge  will  set  cosmically. 

3.  For  the  heliacal  rising  and  setting,  screw  the  quadrant  of 
altitude  over  the  latitude,  turn  the  globe  eastward  on  its  axis  till 
the  sun's  place  cuts  the  quadrant  twelve  degrees  below  the  hori- 
zon ;  then  all  the  stars  of  the  first  magnitude,  along  the  eastern 
edge  of  the  horizon,  will  rise  heliacally ;  and,  by  continuing  the 
motion  of  the  globe  eastward  till  the  sun's  place  interects  the 
quadrant  in  13,  14,  15,  &c.  degrees  below  the  horizon,  you  will 
find  all  the  stars  of  the  second,  third,  fourth,  &c.  magnitudes,  which 
rise  heliacally  on  that  day.  By  turning  the  globe  westward  on 
its  axis,  in  a  similar  manner,  and  bringing  the  quadrant  to  the 
western  egde  of  the  horizon,  you  will  find  all  the  stars  that  set 
heliacally. 

Examples.  1.  What  stars  rise  and  set  cosmically  at  Edin- 
burgh, on  the  11th  of  June? 

tRnswer.  The  bright  star  in  Castor,  Aldebaran  in  Taurus,  Fomalhaut  in  the 
southern  Fish,  &c.  rise  cosmically;  those  stars  in  the  body  of  Leo  Minor,  the  arm 
of  Virgo,  the  right  foot  of  Bootes,  part  of  the  Centaur,  &c.  set  cosmically. 

2.  What  stars  rise  and  set  acronically  at  Drontheim  in  Norway, 
latitude  63°  26'  N.  On  the  18th  May? 

Answer.  Altair  in  the  Eagle,  the  head  of  the  Dolphin,  &c.  rise  acronically;  and 
Aldebaran  in  Taurus,  Betelgeux  in  Orion,  &c.  set  acronically. 

3.  What  star  of  the  first  magnitude  rises  heliacally  at  London, 
on  the  7th  of  October? 

4.  What  star  of  the  first  magnitude  sets  heliacally  at  London, 
on  the  5th  of  May  ? 

5.  What  stars  rise  and  set  acronically  at  London,  on  the 
26th  of  September  ? 

6.  What  stars  rise  and  set  cosmically  at  London,  on  the  23d 
of  March? 


husbandry;  for  the  knowlegde  of  which  the  ancients  had  of  the  motions  of  the 
heavenly  bodies  was  not  sufficient  to  adjust  the  true  length  of  the  year ;  and,  as 
the  returns  of  the  seasons  depends  upon  the  approach  of  the  sun  to  the  tropical 
and  equinoctial  points,  so  they  made  use  of  these  risings  and  settings  to  determine 
the  commencement  of  the  different  seasons,  the  time  of  the  overflowing  of  the 
Nile,  &c.  The  knowledge  which  the  moderns  have  acquired  of  the  motions  of  the 
heavenly  bodies  renders  such  observations  as  the  ancients  attended  to  in  a  great 
measure  useless ;  and,  instead  of  watching  the  rising  and  setting  of  particular  stars 
for  any  remarkable  season,  they  can  sit  by  the  fire-side  and  consult  an  almanac. 


Chap.  11. 


THE   CELESTIAL  GLOBE. 


281 


PROBLEM  LXXVII. 


To  illustrate  the  precession  of  the  equinoxes. 

Observations.  All  the  stars  in  the  different  constellations 
continually  increase  in  longitude  ;  consequently  either  the  whole 
starry  heavens  have  a  slow  motion  from  west  to  east,  or  the  equi- 
noctial points  have  a  slow  motion  from  east  to  west.  In  the  time 
of  Meton*,  the  first  star  in  the  constellation  Aries,  now  marked  /3, 
passed  through  the  vernal  equinox,  whereas  it  is  now  upwards  of 
30t  degrees  to  the  eastward  of  it. 

Illustration.  Elevate  the  north  pole  90  degrees  above  the 
horizon,  then  will  the  equinoctial  coincide  with  the  h  ^rizon  ;  bring 
the  polej  of  the  ecliptic  to  that  part  of  the  brass  meridian  which 
is  numbered  from  tlie  north  pole  towards  the  equinoctial,  and 
make  a  mark  upon  the  brass  meridian  above  it ;  let  this  mark  be 
considered  as  the  pole  of  the  world,  let  the  equinoctial  represent 
the  ecliptic,  and  let  the  ecliptic  be  considered  as  the  equinoctial ; 
then  count  38|-  degrees,  the  complement  of  the  latitude  of  London, 
from  this  pole  upwards,  and  mark  where  the  reckoning  ends,  which 
will  be  at  Ib'^  on  the  brass  meridian,  from  the  southern  point  of 
the  horizon  ;  this  mark  will  stand  over  the  latitude  of  London. 

Now  turn  the  globe  gently  on  its  axis  from  east  to  west,  and 
the  equinoctial  points  will  move  the  same  w^ay,  while,  at  the  sanie 
time,  the  pole  of  the  world|l  will  describe  a  circle  round  the  pole 
of  the  ecliptic§  of  46'  56'  in  diameter;  this  circle  will  be  completed 


*  Meton  was  a  famous  mathematician  of  Athens,  who  flourished  about  432  years 
before  Christ.  In  a  book  called  Enneadecaterides  or  cycle  of  19  years,  he  endeav- 
oured to  adjust  the  course  of  the  sun  and  of  the  moon  ;  and  attempted  to  show  that 
the  solar  and  lunar  years  could  regularly  begin  from  the  same  point  in  the  heavens. 

t  If  the  precession  of  the  equinoxes  be  50^'  in  a  year,  and  if  the  equinoctial  colure 
passed  through  /3  Arietis,  430  years  before  Christ,  the  longitude  of  this  star  ought 
now,  (1304)  io  be  31°  10'  53"  ;  for,  I  year :  50i"  :  :  2234  years  (=430 -f- 1804)  : 
31-^  10'  53"  ;  and  this  longitude  is  not  far  from  the  truth. 

X  The  pole  of  the  ecliptic  is  that  point  on  the  globe,  in  the  arctic  circle,  where  the 
circular  lines  meet. 

II  Let  it  be  remembered  that  the  pole  of  the  ecliptic  on  the  globe  here  represents 
the  pole  of  the  world. 

§  Take  notice,  that  the  extremity  of  the  globe's  axis  here  represents  the  pole  of 
the  ecliptic. 

3G 


282 


PROBLEMS  PERFORMED  BY 


Part  III. 


in  a  Platonic  year*,  consisting  of  25,791  years,  at  the  rate  of 
50i  seconds  in  a  year,  and  the  pole  of  the  heavens  will  vary  its 
situation  a  small  matter  every  year.  When  12,895^  years,  being 
half  the  Platonic  year,  are  completed,  (which  may  be  known  by 
turning  the  globe  half  round,  or  till  the  point  Aries  coincides  with 
the  eastern  point  of  the  horizon,)  that  point  of  the  heavens  which 
is  now  8|  degrees  south  of  the  zenith  of  London,  will  be  the  north 
polef,  as  may  be  seen  by  referring  to  the  mark  which  was  made 
over  75  degrees  on  the  meridian. 

PROBLEM  LXXVIIL 

To  find  the  distances  of  the  stars  from  each  other  in  degrees. 

Rule.  Lay  the  quadrant  of  altitude  over  any  two  stars,  so 
that  the  division  marked  o  may  be  on  one  of  the  stars ;  the  de- 
grees between  them  will  show  their  distance,  or  the  angle  which 
these  stars  subtend,  as  seen  by  a  spectator  on  the  earth. 

Examples.  L  What  is  the  distance  between  Vega  in  Lyra, 
and  altair  in  the  Eagle. 

Answer.    34  degrees. 

2.  Required  the  distance  between  /3  in  the  Bull's  Horn,  and  / 
Bellatrix  in  Orion's  shoulder. 

3.  What  is  the  distance  between  /3  in  Pollux,  and  a  in  Procyon  ? 

4.  What  is  the  distance  between  jj,  the  brightest  of  the  Plei- 
ades, and  iS  in  the  Great  Dog's  Foot  ? 

5.  What  is  the  distance  between  s  in  Orion's  Girdle,  and  ^  in 
Cetus? 

6.  What  is  the  distance  between  Arcturus  in  Bootes,  and  p  in 
the  right  shoulder  of  Serpentarius  ? 


*  A  Platonic  year  is  a  period  of  time  determined  by  the  revolution  of  the  equi- 
noxes ;  this  period  being  once  completed,  the  ancients  were  of  opinion  that  the 
world  was  to  begin  anew,  and  the  same  series  of  things  to  return  over  again.  See 
the  64th  Definition,  page  37. 

t  See  page  134. 


Chap.  II. 


THE  CELESTIAL  GLOBE. 


283 


PROBLEM  LXXIX. 


To  find  what  stars  lie  in  or  near  the  moorHs  path,  or  what  stars  the 
moon  can  eclipse,  or  make  a  near  approach  to. 

Rule.  Find  the  moon's  longitude  and  latitude,  or  her  right 
ascension  and  dechnation,  in  an  ephemeris,  for  several  days,  and 
mark  the  moon's  places  on  the  globe  (as  directed  in  Problems 
LXVIII.  or  LXVII.)  ;  then  by  laying  a  thread,  or  the  quadrant 
of  altitude,  over  these  places,  you  will  see  nearly  the  moon's 
path,*  and  consequently  what  stars  lie  in  her  way. 

Examples.  1.  What  stars  were  in,  or  near,  the  moon's  path, 
on  the  10th,  Ilth,  13th,  and  16th  of  December,  1805? 

10th,  #'s  longitude  a  '^0^  12'  latitude  3°  34'  S. 

11th,  -        TTK  4  22  -  ■     -  4  25  S. 

13th,  -        -=  1  39  -        -  5  15  S. 

16th,         -        TTilO  11  -        -  4  26  S. 

Answer.  The  stars  will  be  found  to  be  Cor  Leonis  or  Regulus,  Spica  Virginis, 
a  in  Libra,  &c.    See  page  47,  White's  Ephemeris. 

2.  On  the  1st,  2d,  3d,  4th,  and  5th  of  August,  1826,  what  stars 
will  lie  near  the  moon's  way  ? 

1st,  fj's  right  ascension  108°  14  declination  18°  40'  N. 

2d,        -       -          121   25  -       -  15  51  N. 

3d,         -       -          134  29  -       -  12  10  N. 

4th,        -       -          147  24  -       -  7  49  N. 

5th,       -      -          160   16  -      -  3  0  N. 


*  The  situation  of  the  moon's  orbit  for  any  particular  day  may  be  found  thus : 
find  the  place  of  the  moon's  ascending  node  in  the  Ephemeris,  mark  that  place  and 
its  antipodes  (being  the  ascending  node)  on  the  globe ;  half  the  way  between  these 
points  make  marks  5°  20'  on  the  north  and  south  side  of  the  ecliptic,  viz.  let  the 
northern  mark  be  between  the  ascending  and  descending  node,  and  the  southern 
between  the  descending  and  ascending  node ;  a  thread  tied  round  these  four  points 
will  show  the  position  of  the  moon's  orbit. 


284 


PROBLEMS  PERFORMED  BY 


Part  III. 


PROBLEM  LXXX. 

Given  the  latitude  of  the  place  and  the  day  of  the  month,  to  find 
^      what  planets  will  he  above  the  horizon  after  sun-setting. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place ;  find  the  sun's  place  in 
the  ecliptic,  and  bring  it  to  the  western  part  of  the  horizon,  or  to 
ten  or  twelve  degrees  below;  then  look  in  the  Ephemeris  for  that 
day  and  month,  and  you  will  find  what  planets  are  above  the 
horizon,  such  planets  will  be  fit  for  observation  on  that  night. 

Examples.  1.  Were  any  of  the  planets  visible  after  the  sun 
had  descended  ten  degrees*  below  the  horizon  of  London,  on 
the  first  of  December,  1805?   Their  longitudes  being  as  follow  : 

^    8s  22^  30  u    8s  L5  27  #'s  longitude  at 

9    9  23    40  >,    6   24  50       midnight  Os  9° 

^    8  25    21  iji    6  24    5  ^ 

Jlnswer.    Venus  and  the  moon  were  visible. 

2.  What  planets  will  be  above  the  horizon  of  London  when 
the  sun  has  descended  ten  degrees  be!ow%  on  the  first  of  January, 
1826?    Their  longitudes  being  as  follow  : 

^    9s  9°  25'  u    5s  14°  27°'  ^'s  longitude  at 

2    8  24    13  ^    2   16  44       midnight  6s  17°  31'. 

^    6  22  19  ijt    9   19  29 


PROBLEM  LXXXI. 

Given  the  latitude  af  the  place,  day  of  the  month,  and  hour  of  the 
night  or  morning,  to  find  what  planets  will  he  visible  at  that 
hour. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place  ;  find  the  sun's  place  in 
the  ecliptic,  bring  it  to  the  brass  meridian,  and  set  the  index  of 


*  The  planets  are  not  visible  till  the  sun  is  a  certain  number  of  desrees  belovi^  the 
h;Orizon,  and  these  degrees  are  variable  according  to  the  brightness  of  the  planets. 
Mercury  becomes  visible  when  the  sun  is  about  ten  degrees  below  the  horizon  ; 
Venus  when  the  sun's  depression  is  5  degrees  j  Mars  U*^  30' j  Jupiter  10®; 
Saturn  11^;  and  the  Georgian  17°  30'. 


Chap,  II. 


THE  CELESTIAL  GLOBE. 


285 


the  hour-circle  to  twelve  :  then,  if  the  given  time  be  before  noon, 
turn  the  globe  eastward  till  the  index  has  passed  over  as  many 
hours  as  the  time  wants  of  noon  ;  but  if  the  given  time  be  past 
noon,  turn  the  globe  westward  on  its  axis  till  the  index  has  passed 
over  as  many  hours  as  the  time  is  past  noon  ;  let  the  globe  rest 
in  this  position,  and  look  in  the  Ephemeris  for  the  longitudes^'  of 
the  planets,  and,  if  any  of  them  be  in  the  signs  which  are  above 
the  horizon,  such  planet  will  be  visible. 

Examples.  1.  On  the  first  of  December,  1805,  the  longitudes 
of  the  planets,  by  an  ephemejis,  were  as  follow :  were  any  of 
them  visible  at  London  at  five  o'clock  in  the  morning? 

^    8s  22"  30'  u    8s  15"  27'  ©'s  longitude  at 

9    9  22  40  1?    6  24  50       midnight  Os  9  15'. 

^    8  25  21  ]j[    6  24  5 

Answer.  Saturn  and  the  Georgium  Sidus  were  visible,  and  both  nearly  in  the 
same  point  of  the  heavens,  near  the  eastern  horizon ,  Saturn  was  a  httle  to  the  ncrth 
of  the  Georgian. 

2.  On  the  first  of  June,  1826,  the  longitudes  of  the  planets  in 
the  fourth  page  of  the  Nautical  Almanc  are  as  follow  :  will  any 
of  them  be  visible  at  London  at  ten  o'clock  in  the  evening? 

^    Is  18°    4'  Zf    5s   5°  .52'  f)'s  longitude  at 

2    3    1  45  p>    2  23  27       midnight  Os  30°  5'. 

^    7    6    2  iji    9  23  38 


PROBLEM  LXXXII. 

The  latitude  of  the  place  and  day  of  the  month  heing  given,  to  find 
how  long  Venus  rises  before  the  sun  when  she  is  a  morning 
star,  and  how  long  she  sets  after  the  sun  when  she  is  an  evening 
star. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place ;  find  the  latitude  and 
longitude  of  Venus  in  an  ephemeris,  and  mark  her  place  on  the 
globe  ;  find  the  sun's  place  in  the  ecliptic,  and  bring  it  to  the  brass 
meridian ;  then,  if  the  place  of  Venus  be  to  the  right  hand  of  the 


*  It  is  not  necessary  to  give  the  latitudes  of  the  planets  in  this  problem ;  for  if 
the  signs  and  degrees  of  the  ecliptic  in  which  their  longitudes  are  situated  be  above 
the  horizon,  the  planets  will  likewise  be  above  the  horizon. 


286 


PROBLEMS  PERFORMED  BY 


Part  III. 


meridian,  she  is  an  evening  star ;  if  to  the  left  hand,  she  is  a  morn- 
ing star. 

When  Venus  is  an  evening  star.  Bring  the  sun's  place  to  the 
western  edge  of  the  horizon,  and  set  the  index  of  the  hour-circle 
to  twelve;  turn  the  globe  westward  on  its  axis  till  Venus  coin- 
cides with  the  western  edge  of  the  horizon  ;  and  the  hours  passed 
over  by  the  index  will  show  how  long  Venus  sets  after  the  sun. 

When  Venus  is  a  morning  star.  Bring  the  sun's  place  to  the 
eastern  edge  of  the  horizon,  and  set  the  index  of  the  hour-circle 
to  twelve  ;  turn  the  globe  eastward  on  its  axis  till  Venus  comes  to 
the  eastern  edge  of  the  horizon,  and  the  hours  passed  over  by  the 
index  will  show  how  long  Venus  rises  before  the  sun. 

Note.  The  same  rule  will  serve  for  Jupiter  by  marking  his 
place  instead  of  that  of  Venus. 

Examples.  1.  On  the  first  of  March  1805,  the  longitude  of 
Venus  was  10  signs,  18  deg.  14  min.,  or  18  deg.  14  min.  in  Aqua- 
rius, latitude  0  deg.  52  min.  south :  was  she  a  morning  or  an  eve- 
ning star  ?  If  a  morning  star,  how  long  did  she  rise  before  the 
sun  at  London ;  if  an  evening  star,  how  long  did  she  shine  after 
the  sun  set  ? 

Answer.  Venus  was  a  morning  star,  and  rose  three  quarters  of  an  hour  before 
the  sun. 

2.  On  the  25th  of  October,  1805,  the  longitude  of  Jupiter  was 
8  signs,  7  deg.  26  min.,  or  7  deg.  26  min.  in  Sagittarius,  latitude 
0  deg.  29  min.  north :  whether  was  he  a  morning  or  an  evening 
star  ?  If  a  morning  star,  how  long  did  he  rise  before  the  sun  at 
London  ?  If  an  evening  star,  how  long  did  he  shine  after  the  sun 
set? 

Answer.  Jupiter  was  an  evening  star,  and  set  1  hour  and  20  minutes  after  the 
sun. 

3.  On  the  first  of  January,  1826,  the  longitude  of  Venus  will  be 
8  signs,  24  deg.  13  min.,  latitude  0  deg.  21  min.  north ;  will  she 
be  an  evening  or  a  morning  star  ?  If  she  be  a  morning  star,  how 
long  will  she  rise  before  the  sun  at  London  ?  If  an  evening  star, 
how  long  will  she  shine  after  the  sun  sets  ? 

4.  On  the  7th  of  July,  1826,  the  longitude  of  Jupiter  will  be 
5  signs,  10  deg.  27  min.,  latitude  1  deg.  8  min.  north ;  will  he  be 
a  morning  or  an  evening  star  1  If  he  be  a  morning  star,  how 
long  will  he  rise  before  the  sun?  If  an  evening  star,  how  long 
will  he  shine  after  the  sun  sets  ? 


Chap,  II. 


THE  CELESTIAL  GLOBE. 


287 


PROBLEM  LXXXIII. 

The  latitude  of  a  place  and  day  of  the  month^  being  given,  to  find 
the  meridian  altitude  of  any  star  or  planet. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place ;  then, 

For  a  star.  Bring  the  given  star  to  that  part  of  the  brass 
meridian,  which  is  numbered  from  the  equinoctial  towards  the 
poles ;  the  degrees  on  the  meridian  contained  between  the  star 
and  the  horizon  will  be  the  altitude  required. 

For  the  moon  or  a  planet.  Look  in  an  ephemeris  for  the  planet's 
latitude  and  longitude,  or  for  its  right  ascension  and  declination, 
for  the  given  month  and  day,  and  mark  its  place  on  the  globe, 
(as  in  Prob.  LXVIII.  or  LXVII.);  bring  the  planet's  place  to  the 
brass  meridian ;  and  the  number  of  degrees  between  that  place 
and  the  horizon  will  be  the  altitude. 

Examples.  I.  What  is  the  meridian  altitude  of  Aldebaran  in 
Taurus,  at  London  ? 

Answer.    54°  36'. 

2.  What  is  the  meridian  altitude  of  Arcturus  in  Bootes,  at  Lon- 
don? 

3.  On  the  first  of  February  1826,  the  longitude  of  Jupiter  will 
be  5  signs,  12  deg.  45  min.,  and  latitude  1  deg.  21  min.  north ; 
what  will  his  meridian  altitude  be  at  London  ? 

4.  On  the  first  of  November  1826,  the  longitude  of  Saturn  will 
be  3  signs  5  deg.  58  min.  and  latitude  0  deg.  59  min.  south ;  what 
will  his  meridian  altitude  be  at  London  ? 

5.  On  the  16th  of  May  1826,  at  the  time  of  the  moon's  passage 
over  the  meridian  of  Greenwich,  her  right  ascension  is  169°  48' 


*  The  meridian  altitudes  of  the  stars  on  the  globe,  in  the  same  latitude,  are  in- 
variable ;  therefore,  when  the  meridian  altitude  of  a  star  is  sought,  the  day  of  the 
month  need  not  be  attended  to. 


288 


PROBLEMS  PERFORMED  BY 


Part  III. 


and  declination  1°  4'  south;  required  her  meridian  altitude  at 
Greenwich  ?^ 

6.  On  the  11th  of  December  1826,  the  moon  will  pass  over 
the  meridian  of  Greenwich  at  3  minutes  past  10  o'clock  in  the 
evening  ;  required  her  meridian  altitude  ? 

The  #'s  right  ascension  at  noon  being  44°  7',  declination  17°  27"  N. 
Do.  at  midnight       -       -       -    50  14       -       -     18  32  N. 

PROBLEM  LXXXIV. 

To  find  all  those  places  on  the  earth  to  which  the  moon  will  he 
nearly  vertical  on  any  given  day. 

Rule.  Look  in  an  ephemeris  for  the  moon's  latitude  and  lon- 
gitude for  the  given  day,  and  mark  her  place  on  the  globe  (as  in 
Prob.  LXVIIl.) ;  bring  this  place  to  that  part  of  the  brass  meridian 
which  is  numbered  from  the  equinoctial  towards  the  poles,  and 
observe  the  degree  above  it ;  for  all  places  on  the  earth  having 
that  latitude  will  have  the  moon  vertical  (or  nearly  so)  when  she 
comes  to  their  respective  meridians. 

Or  :  Take  the  moon's  declination  from  page  VI.  of  the  Nau- 
tical Alman  ic,  and  mark  whether  it  be  north  or  south,  then  by  the 
terrestrial  globe,  or  by  a  map,  find  all  places  having  the  same 
number  of  degrees  of  latitude  as  are  contained  in  the  moon's  de- 
clination, and  those  will  be  the  places  to  which  the  moon  will  be 


*  By  the  Nautical  Almanac,  the  moon  will  pass  over  the  meridian  at  38  minutes 
past  7  o'clock  in  the  evening,  on  the  J  6th  of  May  1826. 

169°  48'  #'s  right  ascension  at  midnight — DecHnation  1°  4"  S. 
163   16  do.  at     -       -       -    noon     -     ditto     -    1   30  N. 


6   32  increase  in  12  hours  from  noon  -       -    2  34 

12  h.  :  6='  32':  :  7  h.  38':  4°  9' ;  12  h.  :  2°  34':  :7h.  38':  1°37'; 
hence  163=*  16'  +  4°  9'  =  167°  hence  1°  30'— 1°  37'  =  0°  T  S. 
25'  the  moon's  right  ascension  at  the  moon's  declination  at  38  min- 
38  minutes  past  7.  utes  past  7. 

The  places  of  the  planets  may  be  taken  out  of  the  Ephemeris  for  noon  without 
sensible  error,  because  their  decUnations  vary  less  than  that  of  the  moon. 

The  moon  will  have  the  greatest  and  least  meridian  altitude  to  all  the  inhabitants 
north  of  the  equator,  when  her  ascending  node  is  in  Aries;  for  her  orbit  making 
an  angle  of  with  the  ecliptic,  her  greatest  altitude  will  be  5\  more  than  the 
greatest  meridional  altitude  of  the  sun,  and  her  least  meridional  altitude  5|°  less 
than  that  of  the  sun.  The  greatest  altitude  of  the  sun  at  London  is  62" ;  the  moon's 
greatest  altitude  is  therefore  67°  20'.  The  least  meridional  altitude  of  the  sun  at 
London  is  15°;  the  least  meridional  altitude  of  the  moon  is  therefore  9"  40^. 


Chap,  II. 


THE  CELESTIAL  GLOBE. 


289 


successively  vertical  on  the  given  day.  If  the  moon's  declination 
be  north,  the  places  will  be  in  north  latitude  ;  if  the  moon's  declin- 
ation be  south,  they  will  be  in  south  latitude. 

Examples.  1.  On  the  15th  of  October,  1805,  the  moon's  lon- 
gitude at  midnight  was  3  signs,  29  deg.  14  min.,  and  her  latitude  1 
deg.  35  min.  south;  over  what  places  did  she  pass  nearly  vertical? 

Answer.  From  the  moon's  latitude  and  longitude  being  given,  her  dedination 
may  be  found  by  the  globe  to  be  about  19"  north.  The  moon  was  vertical  at  Porto 
Rico,  St.  Domingo,  the  north  of  Jamaica,  Owhyhee,  &c. 

2.  On  the  9th  of  September,  1826,  the  moon's  longitude  at 
midnight  will  be  8  signs,  30  deg.,  and  her  latitude  2  deg.  48  min. 
north ;  over  what  places  on  the  earth  will  she  pass  nearly  vertical? 

3.  What  is  the  greatest  north  declination  which  the  moon  can 
possibly  have,  and  to  what  places  will  she  be  then  vertical  ? 

4.  What  is  the  greatest  south  declination  which  the  moon  can 
possibly  have,  and  to  what  places  will  she  be  then  vertical  ? 


PROBLEM  LXXXV. 

Given  the  latitude  of  a  place,  day  of  the  month,  and  the  altitude  of 
a  star,  to  find  the  hour  of  the  night,  and  the  star's  azimuth. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place,  and  screw  the  quadrant 
of  altitude  upon  the  brass  meridian  over  that  latitude :  find  the 
sun's  place  in  the  ecliptic,  bring  it  to  the  brass  meridian,  and  set 
the  index  of  the  hour-circle  to  twelve ;  brinsj  the  lower  end  of  the 
quadrant  of  altitude  to  that  side  of  the  meridian*  on  which  the  star 
was  situated  when  observed ;  turn  the  globe  westward  till  the 
centre  of  the  star  cuts  the  given  altitude  on  the  quadrant ;  count 
the  hours  which  the  index  has  passed  over,  and  they  will  show 
the  time  from  noon  when  the  star  has  the  given  altitude  :  the  quad- 
rant will  intersect  the  horizon  in  the  required  azimuth. 

Examples.    1.  At  London,  on  the  28th  of  December,  the  star 


*  It  is  necessary  to  know  on  which  side  of  the  meridian  the  star  is  at  the  time  of 
observation,  because  it  will  have  the  same  altitude  on  both  sides  of  it.  Any  star 
may  be  taken  at  pleasure,  but  it  is  best  to  take  one  not  too  near  the  meridian,  be- 
cause for  some  time  before  the  star  comes  to  the  meridian,  and  after  it  has  passed 
it,  the  altitude  varies  very  little. 

37 


290 


PROBLEMS  PEliFOIlMED  BY 


Part  III. 


Deneb  in  the  Lion's  tail,  marked  /3,  was  observed  to  be  40°  above 
the  horizon,  and  east  of  the  meridian  ;  what  hour  was  it,  and  what 
was  the  star's  azimuth  ? 

tSnswer.  By  bringing  the  sun's  place  to  the  meridian,  and  turning  the  globe 
westward  on  its  axis  till  the  star  cuts40  degrees  of  the  quadrant  east  of  the  meridian, 
the  index  will  have  passed  over  14  hours;  consequently,  the  star  has  40  degrees  of 
altitude  east  of  the  meridian,  14  hours  from  noon  or  at  two  o'clock  in  the  morning. 
Its  azimuth  will  be  62^  degrees  from  the  south  towards  the  east. 

2.  At  London,  on  the  28th  of  December,  the  star  13,  in  the 
Lion's  tail,  was  observed  to  be  westward  of  the  meridian,  and  to 
have  40  degrees  of  altitude  :  what  hour  was  it,  and  what  was  the 
star's  azimuth  ? 

t^nswer.  By  turning  the  globe  westward  on  its  axis  till  the  star  cuts  40  degrees 
of  the  quadrant  ivest  of  the  meridian,  the  index  will  have  passed  over  20  hours  ;  con- 
sequently, the  star  has  40  degrees  of  altitude  west  of  the  meridian,  20  hours  from 
noon,  or  at  eight  o'clock  in  the  morning.  Its  azimuth  will  be  62^°  from  the  south 
towards  the  west. 

3.  At  London,  on  the  1st  of  September,  the  altitude  of  Benet- 
nach  in  Ursa  Major,  marked  ^,  was  observed  to  be  36  degrees 
above  the  horizon,  and  west  of  the  meridian  ;  what  hour  was  it, 
and  what  was  the  star's  azimuth? 

4.  On  the  21st  of  December  the  altitude  of  Sirius,  when  west 
of  the  meridian  at  London,  was  observed  to  be  8  degrees  above 
the  horizon  ;  what  hour  was  it,  and  what  was  the  star's  azimuth  ? 

5.  On  the  12th  of  August,  Menkar  in  the  Whale's  jaw,  marked 
a,  was  observed  to  be  37  degrees  above  the  horizon  of  London, 
and  eastward  of  the  meridian  ;  what  hour  was  it,  and  what  was 
the  star's  azimuth  ? 


PROBLEM  LXXXVI. 

Given  the  latitude  of  a  place,  day  of  the  month,  and  hour  of  the 
day,  to  find  the  altitude  of  any  star,  and  its  azimuth. 

Rl'le.  Elevate  the  pole  so  many  degrees  above  the  horizon  as 
are  equal  to  the  latitude  of  the  place,  and  screw  the  quadrant  of 
altitude  upon  the  brass  meridian  over  that  latitude  ;  find  the  sun's 
place  in  the  ecliptic,  bring  it  to  the  brass  meridian,  and  set  the 
index  of  the  hour-circle  to  twelve  ;  then,  if  the  given  time  be  be- 
fore noon,  turn  the  globe  eastward  on  its  axis  till  the  index  has 
passed  over  as  many  hours  as  the  time  wants  of  noon  ;  if  the  time 
be  past  noon,  turn  the  globe  westward  till  the  index  has  passed 
over  as  many  hours  as  the  time  is  past  noon :  let  the  globe  rest 


Chap.  II. 


THE   CELESTIAL  GLOBE. 


291 


in  this  position,  and  move  the  quadrant  of  altitude  till  its  graduated 
edge  coincides  with  the  centre  of  the  given  star;  the  degrees  on 
the  quadrant,  from  the  horizon  to  the  star,  w^ill  be  the  altitude; 
and  the  distance  from  the  north  and  south  point  of  the  horizon  to 
the  quadrant,  counted  on  the  horizon,  will  be  the  azimuth  from 
the  north  and  south. 

Ex\MPLES.  1.  What  are  the  altitude  and  azimuth  of  Capella 
at  Rome,  when  it  is  live  o'clock  in  the  morning  on  the  second  of 
December  ? 

Answer.  The  altitude  is  41°  58',  and  the  azimuth  60'^  SCK  from  the  north  to- 
wards the  west. 

2.  Required  the  altitude  and  azimuth  of  Altair  in  Aquila  on 
the  6th  of  October,  at  nine  o'clock  in  the  evening,  at  London  ? 

3.  On  what  point  of  the  compass  does  the  star  Aldebaran  bear 
at  the  Cape  of  Good  Hope,  on  the  5th  of  March,  at  a  quarter  past 
eight  o'clock  in  the  evening  ;  and  what  is  its  altitude  ? 

4.  Required  the  altitude  and  azimuth  of  Acyone  in  the  Pleiades 
marked  jj,  on  the  2 1st  of  December,  at  four  o'clock  in  the  morn- 
ing at  London  ? 


PROBLEM  LXXXVIL 

Given  the  latitude  of  the  place,  day  of  the  month,  and  azimuth  of  a 
star,  to  find  the  hour  of  the  night  and  the  starts  altitude. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place,  and  screw  the  quadrant 
of  altitude  upon  the  brass  meridian  over  that  latitude  ;  find  the 
sun's  place  upon  the  ecliptic,  bring  it  to  the  brass  meridian,  and 
set  the  index  of  the  hour-circle  to  twelve  ;  bring  the  lower  end  of 
the  quadrant  of  altitude  to  coincide  with  the  given  azimuth  on  the 
horizon,  and  hold  it  in  that  position  ;  turn  the  globe  westward  till 
the  given  star  comes  to  the  graduated  edge  of  the  quadrant,  and 
the  hours  passed  over  by  the  index  will  be  the  time  from  noon ; 
the  degrees  on  the  quadrant,  reckoning  from  the  horizon  to  the 
star,  will  be  the  altitude. 

Examples.  1.  At  London,  on  the  28th  of  December,  the  azi- 
muth of  Deneb  in  the  Lion's  tail  marked  ^,  was  62|^°  from  the 
south  towards  the  west,  what  hour  was  it,  and  what  was  the  star's 
altitude  ? 

^  Answer.  By  turning  the  globe  westward  on  its  axis,  the  index  will  pass  over  20 
hours  before  the  star  intersects  the  quadrant ;  therefore  the  time  will  be  20  hours 


292 


PROBLEMS  PERFORMED  BY 


Part  III. 


from  noon,  or  eight  o'clock  in  the  morning  j  and  the  star's  altitude  will  be  40  de- 
grees. 

2.  At  London,  on  the  5th  of  May,  the  azimuth  of  Cor  Leonis, 
or  Regulus,  marked  ee,  was  74°  from  the  south  towards  the  west; 
required  the  star's  altitude,  and  the  hour  of  the  night. 

3.  On  the  8th  of  October,  the  azimuth  of  the  star  marked  /3, 
in  the  shoulder  of  Auriga,  was  50"  from  the  north  towards  the 
east ;  required  its  altitude  at  London,  and  the  hour  of  the  night. 

4.  On  the  10th  of  September,  the  azimuth  of  the  star  marked 
in  the  Dolphin,  was  20°  from  the  south  towards  the  east ;  required 
its  altitude  at  London,  and  the  hour  of  the  night. 


PROBLEM  LXXXVIIL 

Two  stars  being  gwen,  the  one  on  the  meridian,  and  the  other  on 
the  east  or  west  part  of  the  horizon,  to  find  the  latitude  of  the 
place. 

Rule.  Bring  the  star  which  was  observed  to  be  on  the 
meridian,  to  the  brass  meridian  ;  keep  the  globe  from  turning  on  its 
axis,  and  elevate  or  depress  the  pole  till  the  other  star  comes  to 
the  eastern  or  western  part  of  the  horizon  ;  then  the  degrees  from 
the  elevated  pole  to  the  horizon  will  be  the  latitude. 

Examples.  L  When  the  two  pointers*  of  the  Great  Bear, 
marked  a  and  jS,  or  Dubhe  and  /S,  were  on  the  meridian,  I  observed 
Vega  in  Lyra  to  be  rising ;  required  the  latitude. 

Answer,    'il"  north. 

2.  When  Arcturus  in  Bootes  was  on  the  meridian,  Altair  in 
the  Eagle  was  rising  ;  required  the  latitude. 

3.  When  the  star  marked  /3  in  Gemini  was  on  the  meridian, 
£  in  the  shoulder  of  Andromeda  was  setting ;  required  the  lati- 
tude. 

4.  In  what  latitude  are  and  iS,  or  Sirius  and  /3  in  Canis  Major 
rising,  when  Algenib,  or     in  Perseus,  is  on  the  meridian  ? 


*  These  two  stars  are  called  the  pointers,  because  a  line  drawn  through  themj 
points  to  the  'polar  star  in  Ursa  Minor.    See  page  131. 


Chap.  II. 


THE  CELESTIAL  GLOBE. 


293 


PROBLEM  LXXXIX. 

The  latitude  of  the  place,  the  day  of  the  month,  and  two  stars 
that  have  the  same  azimuth,*  being  given,  to  find  the  hour  of 
the  night. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place,  and  screw  the  quadrant 
of  altitude  upon  the  brass  meridian  over  that  latitude ;  find  the 
sun's  place  in  the  ecliptic,  bring  it  to  the  brass  meridian,  and  set 
the  index  of  the  hour-circle  to  twelve  :  turn  the  globe  on  its  axis 
from  east  to  west  till  the  two  given  stars  coincide  with  the 
graduated  edge  of  the  quadrant  of  altitude  ;  the  hours  passed  over 
by  the  index  will  show  the  time  from  noon  ;  and  the  common 
aximuth  of  the  two  stars  will  be  found  on  the  horizon. 

Examples.  I.  At  what  hour,  at  London,  on  the  first  of  May, 
will  Altair  in  the  Eagle,  and  Vega  in  the  Harp,  have  the  same 
azimuth,  and  what  will  that  azimuth  be  ? 

Answer.  By  bringing  the  sun's  place  to  the  meridian,  &c.  and  turning  the  globe 
westward,  the  index  will  pass  over  15  hours  before  the  stars  coincide  with  the 
quadrant  :  hence  they  will  have  the  same  azimuth  at  15  hours  from  noon,  or  at 
three  o'clock  in  the  morning  ;  aud  the  azimuth  will  be  42^°  from  the  south  towards 
the  east. 

2.  On  the  10th  of  September,  what  is  the  hour  at  London, 
when  Deneb  in  Cygnus,  and  Markab  in  Pegasus,  have  the  same 
azimuth,  and  what  is  the  azimuth  ? 

3.  At  what  hour  on  the  I5th  of  April  will  Arcturus  and  Spica 
Virginis  have  the  same  azimuth  at  London,  and  what  will  that 
azimuth  be  ? 

4.  On  the  20th  of  February,  what  is  the  hour  at  Edinburgh 
when  Capella  and  the  Pleiades  have  the  same  azimuth,  and  what 
is  the  azimuth  ? 


*  To  find  what  stars  have  the  same  azimuth. — Let  a  smooth  rectangular  board 
of  about  a  foot  in  breadth,  and  three  feet  high  (or  of  any  height  you  please),  be 
fixed  perpendicularly  upon  a  stand  ;  draw  a  straight  line  through  the  middle  of  the 
board,  parallel  to  the  sides :  fix  a  pin  in  the  upper  part  of  this  line,  and  make  a  hole 
in  the  board  at  the  lower  part  of  the  Hne  ;  hang  a  thread  with  a  plummet  fixed  to  it 
upon  the  pin,  and  let  the  ball  of  the  plummet  move  freely  in  the  hole  made  in  the 
lower  part  of  the  board  :  set  this  board  upon  a  table  in  a  window,  or  in  the  open  air, 
and  wait  till  the  plummet  ceases  to  vibrate:  then  look  along  the  face  of  the  board, 
and  those  stars  which  are  partly  hid  from  your  view  by  the  thread  will  have  the 
same  azimuth. 


294 


PROBLEMS  PERFORMED  BY 


Part  III. 


5.  On  the  21st  of  December,  what  is  the  hour  at  Dublin  when 
a  or  Algenib  in  Perseus,  and  /3  in  the  Bull's  Horn,  have  the  same 
azimuth,  and  what  is  the  azimuth? 


PROBLEM  XC. 

The  latitude  of  the  place,  the  d^y  of  the  month,  and  two  stars 
that  have  the  same  altitude,  being  given,  to  find  the  hour  of  the 
nigfd. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  place,  and  screw  the  quadrant 
of  altitude  upon  the  brass  meridian  over  that  latitude  ;  find  the 
sun's  place  in  the  ecliptic,  bring  it  to  the  brass  meridian,  and  set 
the  index  of  the  hour-circle  to  twelve,  turn  the  globe  on  its  axis 
from  east  to  west  till  the  two  given  stars  coincide  with  the  given 
altitude  on  the  graduated  edge  of  the  quadrant ;  the  hours  passed 
over  by  the  index  will  be  the  time  from  noon  when  the  two  stars 
have  that  altitude. 

Examples.  1.  At  what  hour  at  London,  on  the  second  of 
September,  will  Markab  in  Pegasus,  and  a  in  the  head  of  An- 
dromeda, have  each  30°  of  altitude  ? 

Answer.  At  a  quarter  past  eight  in  the  evening. 

2.  At  what  hour  at  London,  on  the  5th  of  January,  will  a, 
Menkar,  in  the  Whale's  jaw,  and  a,  Aldebaran,  in  Taurus,  have 
each  35°  of  altitude  ? 

3.  At  what  hour  at  Edinburgh,  on  the  10th  of  November,  will 
a,  Altair  in  the  body  of  the  Eagle,  and  C>  in  the  tail  of  the  Eagle, 
have  each  35°  of  altitude  ? 

4.  At  what  hour  at  Dublin,  on  the  15th  of  May,  will  y\,  Benet- 
nach  in  the  Great  Bear's  tail,  and  v,  in  the  shoulder  of  Bootes, 
have  56°  of  altitude  ? 


PROBLEM  XCL 

The  altitudes  of  two  stars  having  the  same  azimuth,  and  that 
azimuth  being  given,  to  find  the  latitude  of  the  place. 

Rule.  Place  the  graduated  edge  of  the  quadrant  of  altitude 
over  the  tw^o  stars,  so  that  each  star  may  be  exactly  under  its 
given  altitude  on  the  quadrant ;  hold  the  quadrant  in  this  position, 


Chap,  II. 


THE   CELESTIAL  GLOBE. 


295 


and  elevate  or  depress  the  pole  till  the  division  marked  o,  on  the 
lower  end  of  the  quadrant,  coincides  with  the  given  azimuth  on 
the  horizon  :  when  this  is  effected,  the  elevation  of  the  pole  will 
be  the  latitude. 

Examples.  1.  The  altitude  of  Arcturus  was  observed  to  be 
40  deg.,  and  that  of  Cor.  Caroli  68  deg. ;  their  common  azimuth 
at  the  same  time  was  71  deg.  from  the  south  towards  the  east; 
required  the  latitude. 

Answer.    51^  deg.  north. 

2.  The  altitude  of  e  in  Castor  was  observed  to  be  40  deg.,  and 
that  of  /3  in  Procyon  20  deg.  ;  their  common  azimuth  at  the  same 
time  was  73|^  deg.  from  the  south  towards  the  east ;  required  the 
latitude. 

3.  The  altitude  of  a,  Dubhe,  was  observed  to  be  40  deg.,  and 
that  of  y  in  the  back  of  the  Great  Bear  29^  deg.,  their  common 
azimuth  at  the  same  time  was  30  deg.  from  the  north  towards  the 
east ;  required  the  latitude. 

4.  The  altitude  of  Vega,  or  a  in  Lyra,  was  observed  to  be  70- 
deg.,  and  that  of  «  in  the  head  of  Hercules  39^  deg.,  their  com- 
mon azimuth  at  the  same  time  was  60  deg.  from  the  south  towards 
the  west;  required  the  latitude. 


PROBLEM  XCII. 

The  day  of  the  month  being  given,  and  the  hour  when  any  known 
star  rises  or  sets,  to  find  the  latitude  of  the  jilctce. 

Rule.  Find  the  sun's  place  in  the  ecliptic,  bring  it  to  the  brass 
meridian,  and  set  the  index  of  the  hour-circle  to  12 ;  then,  if  the 
given  time  be  before  noon,  turn  the  globe  eastward  till  the  index 
has  passed  over  as  many  hours  as  the  time  wants  of  noon;  but  if 
the  given  time  be  past  noon,  turn  the  globe  westward  till  the  index 
has  passed  over  as  many  hours  as  the  time  is  past  noon  ;  elevate 
or  depress  the  pole  till  the  centre  of  the  given  star  coincides  with 
the  horizon  ;  then  the  elevation  of  the  pole  will  show  the  latitude. 

Examples.  1.  In  what  latitude  does  e,  Mirach,  in  Bootes,  rise 
at  half  past  twelve  o'clock  at  night,  on  the  tenth  of  December  ? 

Jlnswer.    51^  deg.  north. 

2.  In  what  latitude  does  Cor  Leonis,  or  Regulus,  rise  at  10 
o'clock  at  night,  on  the  21st  of  January  ? 

3.  In  what  latitude  does  /g,  Rigel  in  Orion,  set  at  4  o'clock  in 
the  morning,  on  the  twenty- first  of  Deceoiber  ? 


296 


PROBLEMS  PEKFORMED  BY 


Part  III. 


4.  In  what  latitude  does  /3,  Capricornus,  set  at  eleven  o'clock 
at  night  on  the  tenth  of  October  ? 

PROBLEM  XCIII. 

?b  find  on  vShai  day  of  the  year  any  given  star  passes  the  meridian 
at  any  given  hour. 

Rule.  Bring  the  given  star  to  the  brass  meridian,  and  set  the 
index  to  12 ;  then,  if  the  given  time  be  before  noon*,  turn  the 
globe  w^estward  till  the  index  has  passed  over  as  many  hours  as 
the  time  wants  of  noon  ;  but,  if  the  given  time  be  past  noon,  turn 
the  globe  eastward  till  the  index  has  passed  over  as  many  hours- 
as  the  tim,e  is  past  noon ;  observe  that  degree  of  the  ecliptic 
which  is  intersected  by  the  graduated  edge  of  the  brass  meridian, 
and  the  day  of  the  month  answering  thereto,  on  the  horizon,  will 
be  the  day  required. 

Examples.  1.  On  w^hat  day  of  the  month  does  Procyon  come 
to  the  meridian  of  London  at  three  o'clock  in  the  morning  ? 

Jlnswer.  Here  the  time  is  nine  hours  before  noon  ;  the  globe  must  therefore  be 
turned  nine  hours  towards  the  west,  the  point  of  the  echptic  intersected  by  the 
brass  meridian  will  then  be  the  ninth  of  / ,  answering  nearly  to  the  first  of  Decem- 
ber. 

2.  On  what  day  of  the  month,  and  in  what  month  does  es, 
Alderamin,  in  Cepheus,  come  to  the  meridian  of  Edinburgh  at 
ten  o'clock  at  night  ? 

Answer.  Here  the  time  is  ten  hours  afternoon;  the  globe  must  therefore  be 
turned  ten  hours  towards  the  east,  the  point  of  the  ecliptic  intersected  by  the  brass 
meridian  will  then  be  the  17th  of  V(^,  answering  to  the  ninth  of  September. 

3.  On  what  day  of  the  month,  and  in  what  month,  does  /3, 
Deneb,  in  the  Lion's  tail,  come  to  the  meridian  of  Dublin  at  nine 
o'clock  at  night  ? 

4.  On  what  day  of  the  month,  and  in  what  month,  does  Arc- 
turus  in  Bootes  come  to  the  meridian  of  London  at  noon  ? 

5.  On  what  day  of  the  month,  and  in  what  month,  does  5  in  the 
Great  Bear  come  to  the  meridian  of  London  at  midnight  ? 

6.  On  what  day  of  the  month,  and  in  what  month,  does  Alde- 
baran  come  to  the  meridian  of  Philadelphia  at  five  o'clock  in  the 
morning  at  London  ? 


*  If  the  given  star  come  to  the  meridian  at  noon,  the  sun's  place  will  be  found 
under  the  brass  meridian,  without  turning  the  globe  ;  if  the  given  star  come  to  the 
meridian  at  midnight,  the  globe  may  be  turned  either  eastward  or  westward  till  the 
index  has  passed  over  twelve  hours. 


Chap.  II. 


THE  CELESTIAL  GLOBE. 


297 


PROBLEM  XCIV. 

The  day  of  the  month  being  given,  to  find  at  what  hour  any  given 
star  comes  to  the  meridian.* 

Rule.  Find  the  sun's  place  in  the  ediptic,  bring  it  to  the  brass 
meridian,  and  set  the  index  of  the  hour-circle  to  12 ;  turn  the 
globe  westward  on  its  axis  till  the  given  star  comes  to  the  brass 
meridian,  and  the  hours  passed  over  by  the  index  will  be  the  time 
from  noon  when  the  star  culminates. 


Or,  without  the  globe. 

Subtract  the  right  ascension  of  the  sun  for  the  given  day  from 
the  right  ascension  of  the  star,  and  the  remainder  will  be  the  time 
of  the  star's  culminating  nearly.-\ — If  the  sun's  right  ascension 
exceed  the  star's,  add  twenty-four  hours  to  the  star's  before  you 
subtract. 

Examples.  1.  At  what  hour  does  Cor  Leonis,  or  Regulus, 
come  to  the  meridian  of  London  on  the  23d  of  September  ? 

Answer.  The  index  will  pass  over  21|  hours ;  hence  this  star  culminates  or 
comes  to  the  meridian  2l|  hours  after  noon,  or  at  three  quarters  past  nine  o'clock 
in  the  morning. 

2.  At  what  hour  does  Arcturus  come  to  the  meridian  of 
London  on  the  9th  of  February  ? 

AnsvHr.  The  index  will  pass  over  16^  hours ;  hence  Arcturus  culminates  16^ 
hours  after  noon,  or  at  half-past  four  o'clock  in  the  morning. 

3.  Required  the  hours  at  which  the  following  stars  come  to  the 
meridion  of  London  on  the  respective  days  annexed. 


P  Mirach,  October  5th. 

Aldebaran,  Feb.  12th. 
P  Aries,  November  5th. 
s  Taurus,  January  24th. 
4.  At  what  time  did  Sirius  come  to  the  meridian  of  Greenwich 
on  the  I8th  of  December,  1825,  his  right  ascension  being  99"  22' 
49",  and  the  sun's  right  ascension  266°  V  57". 


Bellatrix,  January  9th. 
Menkar,  May  18th. 
e  Draco,  Sept.  22d. 
«  Dubhe,  Dec.  20th. 


*  This  Problem  is  comprehended  in  Problem  LXXI. 
t  Vide  KeitK'8  Trigonometry,  fourth  edition,  p.  273. 

38 


298 


PROBLEMS  PERFORMED  BY 


Part  IIL 


PROBLEM  XCV. 

Given  the  azimuth  of  a  known  star,  the  latitude,  and  the  hour,  to 
find  the  star's  altitude  and  the  day  of  the  month. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon 
as  are  equal  to  the  latitude  of  the  given  place,  screw  the  quadrant 
of  altitude  upon  the  brass  meridian  over  that  latitude,  bring  the 
division  marked  o  on  the  lower  end  of  the  quadrant  to  the  given 
azimuth  on  the  horizon,  turn  the  globe  till  the  star  coincides  with 
the  graduated  edge  of  the  quadrant,  and  set  the  index  of  the 
hour-circle  to  12 ;  then,  if  the  given  time  be  before  noon,  turn 
the  globe  westward  till  the  index  has  passed  over  as  many  hours 
as  the  time  wants  of  noon  ;  if  the  given  time  be  past  noon,  turn 
the  globe  eastward  till  the  index  has  passed  over  as  many  hours 
as  the  time  is  past  noon  ;  observe  that  degree  of  the  ecliptic  which 
is  intersected  by  the  graduated  edge  of  the  brass  meridian,  and 
the  day  of  the  month  answering  thereto,  on  the  horizon,  will  be 
the  day  required. 

Examples.  1.  At  London,  at  ten  o'clock  at  night,  the  azimuth 
of  Spica  Virginis  was  observed  to  be  40  deg.  from  the  south 
towards  the  west ;  required  its  altitude,  and  the  day  of  the  month. 

Answer.  The  star's  altitude  is  20  deg.  and  the  day  is  the  18th  of  June.  The 
time  being  10  hours  past  noon,  the  globe  must  be  turned  ten  hours  towards  the 
east. 

2.  At  London,  at  four  o'clock  in  the  morning,  the  azimuth  of 
Arcturus  was  70  deg.  from  the  south  towards  the  west ;  required 
its  altitude  and  the  day  of  the  month. 

Answer.  Here  the  time  wants  eight  hours  of  noon,  therefore  the  globe  must  be 
turned  eight  hours  westward  :  the  altitude  of  the  star  will  be  found  to  be  40  deg., 
and  the  day  the  12th  of  April. 

3.  At  Edinburgh,  at  eleven  o'clock  at  night,  the  azimuth  of  a 
Serpentarius,  or  Ras  Alhagus,  was  60  deg.  from  the  south  towards 
the  east ;  required  its  altitude,  and  the  day  of  the  month. 

4.  At  Dublin,  at  two  o'clock  in  the  morning,  the  azimuth  of  /3 
Pegasus,  or  Scheat,  was  70  deg.  from  the  north  towards  the  east ; 
required  its  altitude  and  the  day  of  the  month. 


Chap.  II. 


THE  CELSETIAL  GLOBE. 


299 


PROBLEM  XCVI. 

The  altitude  of  two  stars  being  given,  to  find  the  latitude  of  the 

place. 

Rule.  Subtract  each  star's  altitude  from  90  deg. ;  take  suc- 
cessively the  extent  of  the  number  of  degrees,  contained  in  each 
of  the  remainders,  from  the  equinoctial,  with  a  pair  of  compasses; 
with  the  compasses  thus  extended,  place  one  foot  successively  in 
the  centre  of  each  star,  and  describe  arcs  on  the  globe  with  a 
blacklead  pencil ;  these  arcs  will  cross  each  other  in  the  zenith ; 
bring  the  point  of  intersection  to  that  part  of  the  brass  meridian 
which  is  numbered  from  the  equinoctial  towards  the  poles,  and 
the  degree  above  it  will  be  the  latitude.* 

Examples.  1.  At  sea,  in  north  latitude,  I  observed  the  alti- 
tude of  Capella  to  be  30  deg.,  and  that  of  Aldebaran  35  deg. ; 
what  latitude  was  I  in  ? 

Answer.  With  an  extent  of  60  deg.  (=90-= — 30°)  taken  from  the  equinoctial, 
and  one  foot  of  the  compasses  in  the  centre  of  Capella,  describe  an  arc  towards  the 
north;  then  with  55  deg.  (=90° — 55°),  taken  in  a  similar  manner,  and  one  foot  of 
the  compasses  in  the  centre  of  Aldebaran,  describe  an  other  arc,  crossing  the  former; 
the  point  of  intersection  brought  to  the  brass  meridian  will  show  the  latitude  to  be 
20^  deg.  north. 

2.  The  altitude  of  Markab  in  Pegasus  was  30  deg.,  and  that  of 
Altair  in  the  Eagle,  at  the  same  time,  was  65  deg. ;  what  was  the 
latitude,  supposing  it  to  be  north  ? 

3.  In  north  latitude  the  altitude  of  Arcturus  was  observed  to  be 
60  deg.,  and  that  of  /3  or  Deneb,  in  the  Lion's  Tail,  at  the  same 
time,  was  70  deg. ;  what  was  the  latitude  ? 

4.  In  north  latitude,  the  altitude  of  Procyon  was  observed  to 
be  50  deg.,  and  that  of  Betelgeux  in  Orion,  at  the  same  time,  was 
58  deg. ;  required  the  latitude  of  the  place  of  observation. 


*  The  arc  described  in  the  rule  will  intersect  twice ;  and  therefore  if  both  points 
of  intersection  be  within  90  degrees  of  the  elevated  pole,  there  will  be  two  answers 
to  the  problem,  or  the  required  latitude  will  be  ambiguous :  if  only  one  intersection 
be  within  90  degrees  of  the  elevated  pole  there  will  be  no  ambiguity,  as  the  zenith 
must  be  within  90  degrees  of  the  elevated  pole.  If  it  were  unknown  on  which  side 
of  the  equator  the  observations  were  made,  either  pole  may  be  elevated,  and  the 
zenith  or  zeniths  will  be  found  as  before. 


300 


PROBLEMS  PERFORMED  BY 


Part  III. 


PROBLEM  XCVII. 

The  meridian  altitude  of  a  known  star  being  given,  at  any  place 
in  north  latitude,  to  find  the  latitude. 

Rule.  Bring  the  given  star  to  that  part  of  the  brass  meridian 
which  is  numbered  from  the  equinoctial  towards  the  poles ;  count 
the  number  of  degrees  in  the  given  altitude  on  the  brass  meridian 
from  the  star  towards  the  south  part  of  the  horizon,  and  mark 
where  the  reckoning  ends ;  elevate  or  depress  the  pole  till  this 
mark  coincides  with  the  south  point  of  the  horizon,  and  the  ele- 
vation of  the  north  pole  above  the  north  point  of  the  horizon  will 
show  the  latitude. 

Examples.  1.  In  what  degree  of  north  latitude  is  the  merid- 
ian altitude  of  Aldebaran  52|  deg.  ? 

Answer.    53  deg.  36  min.  north. 

2.  In  what  degree  of  north  latitude  is  the  meridian  altitude  of 
one  of  the  pointers  in  Ursa  Major,  90  deg.  ? 

3.  In  what  degree  of  north  latitude  is  y,  in  the  head  of  Draco, 
vertical  when  it  culminates  ? 

4.  In  what  degree  of  north  latitude  is  the  meridian  altitude  of 
f  or  Mirach  in  Bootes,  68  degrees  ? 


PROBLEM  XCVIII. 

The  latitude  of  a  place,  day  of  the  month,  and  hour  of  the  day, 
being  given,  to  find  the  nonagesimal  degree*  of  the  ecliptic, 
its  altitude  and  azimuth,  and  the  medium  coeli. 

Rule.  Elevate  the  north  pole  to  the  latitude  of  the  given 
place,  and  screw  the  quadrant  of  altitude  upon  the  brass  meridian 
over  that  latitude ;  find  the  sun's  place  in  the  ecliptic,  bring  it  to 
the  brass  meridian,  and  set  the  index  of  the  hour-circle  to  12 ; 


+  The  nonagesimal  degree  of  the  ecliptic  is  that  point  which  is  the  most  elevated 
above  the  horizon,  and  is  measured  by  the  angle  vv^hich  the  ecliptic  makes  with  the 
horizon  at  any  elevation  of  the  pole ;  or,  it  is  the  distance  between  the  zenith  of  the 
place  and  the  pole  of  the  ecliptic.  This  angle  is  frequently  used  in  the  calculation 
of  solar  ecUpses.  The  medium  ccEli,  or  mid-heaven,  is  that  point  of  the  ecliptic 
which  is  upon  the  meridian. 


Chap.  II. 


THE  CELESTIAL  GLOBE. 


301 


then  if  the  given  time  be  before  noon,  turn  the  globe  eastward  till 
the  index  has  passed  over  as  many  hours  as  the  time  w^ants  of 
noon  ;  but,  if  the  given  time  be  past  noon,  turn  the  globe  west- 
ward till  the  index  has  passed  over  as  many  hours  as  the  time  is 
past  noon,  and  fix  the  globe  in  this  position  ;  count  90  deg.  upon 
the  ecliptic  from  the  horizon  (either  eastward  or  westward),  and 
mark  where  the  reckoning  ends,  for  that  point  of  the  ecliptic 
will  be  the  nonagesimal  degree,  and  the  degree  of  the  ecliptic  cut 
by  the  brass  meridian  will  be  the  medium  coeli ;  bring  the  grad- 
uated edge  of  the  quadrant  of  altitude  to  coincide  with  the  nona- 
gesimal degree  of  the  ecliptic  thus  found,  and  the  number  of  de- 
grees on  the  quadrant,  counted  from  the  horizon,  will  be  the  alti- 
tude of  the  nonagesimal  degree  :  the  azimuth  will  be  seen  on  the 
horizon. 

Examples.  1.  On  the  21st  of  June,  at  forty-five  minutes  past 
three  o'clock  in  the  afternoon  at  London,  required  the  point  of 
the  ecliptic  which  is  the  nonagesimal  degree,  its  altitude  and  azi- 
muth, the  longitude  of  the  medium  cceH,  and  its  altitude,  &c. 

Jlnswer.  The  nonagesimal  degree  is  10  deg.  in  Leo.  its  altitude  is  54  deg.,  and 
its  azimuth  22  deg.  from  the  south  towards  the  west,  or  nearly  S.  S.  W.  The  mid- 
heaven,  or  point  of  the  ecliptic  under  the  brass  meridian,  is  24  deg.  in  Leo,  and  its 
altitude  above  the  horizon  is  52  deg.  The  degree  of  the  equinoctial  cut  by  the  brass 
meridian,  reckoning  from  the  point  Aries,  is  the  right  ascension  of  the  mid-heaven, 
which  in  this  example  is  146  degrees.  The  rising  point  of  the  echptic  will  be  found 
to  be  10  deg.  in  Scorpio,  and  the  setting  point  10  degrees  in  Taurus.  If  the  grad- 
uated edge  of  the  quadrant  be  brought  to  coincide  with  the  sun's  place,  the  sun's 
altitude  will  be  found  to  be  39  deg.,  and  his  azimuth  78^  deg.  from  the  south  towards 
the  west,  or  nearly  W.  by  S. 

2.  At  London,  on  the  24th  of  April,  at  nine  o'clock  in  the 
morning ;  required  the  point  of  the  ecliptic  which  is  the  nona- 
gesimal degree,  its  altitude  and  azimuth,  the  point  of  the  ecliptic 
which  is  the  mid-heaven,  &c.  &c. 

3.  At  Limerick,  in  52  deg.  22  min.  north  latitude,  on  the  15th 
of  October,  at  5  o'clock  in  the  afternoon ;  required  the  point  of 
the  ecliptic  which  is  the  nonagesimal  degree,  its  altitude  and  azi- 
muth, the  point  of  the  ecliptic  which  is  the  mid-heaven,  &c.  &c. 

4.  At  Dublin,  in  latitude  53  deg.  21  min.  north,  on  the  15th  of 
January,  at  two  o'clock  in  the  afternoon  ;  required  the  longitude, 
altitude  and  azimuth,  of  the  nonagesimal  degree  ;  and  the  longi- 
tude and  altitude  of  the  medium  coeli,  &c.  &c. 


302 


PROBLEMS  PERFORMED  BY 


Part  III. 


PROBLEM  XCIX. 

The  latitude  of  a  place,  day  of  the  month,  and  the  hour,  together 
with  the  altitude  and  azimuth  of  a  star,  being  given,  to  find  the 
star. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon  as 
are  equal  to  the  latitude  of  the  place,  and  screw  the  quadrant  of 
altitude  on  the  brass  meridian  over  that  latitude :  find  the  sun's 
place  in  the  ecliptic,  bring  it  to  the  brass  meridian,  and  set  the  in- 
dex of  the  hour-circle  to  12 ;  then,  if  the  given  time  be  before 
noon,  turn  the  globe  eastward  till  the  index  has  passed  over  as 
many  hours  as  the  time  wants  of  noon  ;  but,  if  the  time  be  past 
noon,  turn  the  globe  westward  till  the  index  has  passed  over  as 
many  hours  as  the  time  is  past  noon  j  let  the  globe  rest  in  this 
position,  and  bring  the  division  marked  O  on  the  quadrant  to  the 
given  azimuth  on  the  horizon  ;  then,  immediately  under  the  given 
altitude  on  the  graduated  edge  of  the  quadrant,  you  will  find  the 
star. 

Examples.  1.  At  London,  on  the  21st  of  December,  at  four 
o'clock  in  the  morning,  the  altitude  of  a  star  was  50",  and  its  azi- 
muth was  37°  from  the  south  towards  the  east,  required  the  name 
of  the  star. 

Answer.    Deneb,  or  /3  in  the  Lion's  tail. 

2.  The  altitude  of  a  star  was  27°,  its  azimuth  761°  from  the 
south  towards  the  west,  at  1 1  o'clock  in  the  evening  at  London, 
on  the  11th  of  May ;  what  star  was  it  ? 

3.  At  London,  on  the  21st  of  December,  at  four  o'clock  in  the 
morning,  the  altitude  of  a  star  was  eight  degrees,  and  its  azimuth 

from  the  south  towards  the  west ;  required  the  name  of  the 

star. 

4.  At  London,  on  the  first  of  September,  at  nine  o'clock  in  the 
evening,  the  altitude  of  a  star  was  47°,  and  its  azimuth  73°  from 
the  south  towards  the  east ;  required  the  name  of  the  star. 


Chap.  11. 


THE  CELESTIAL  GLOBE. 


303 


PROBLEM  C. 

To  find  the  time  of  the  moon^s  southing,  or  coming  to  the  meridian 
of  any  place,  on  any  given  day  of  the  month. 

Rule.  Elevate  the  pole  so  many  degrees  above  the  horizon  as 
are  equal  to  the  latitude  of  the  given  place  ;  find  the  moon's  lati- 
tude and  longitude,  or  her  right  ascension  and  declination,  from 
an  ephemeris,  and  mark  her  place  on  the  globe  ;  bring  the  sun's 
place  to  the  brass  meridian,  and  set  the  index  of  the  hour-circle  to 
12  ;  turn  the  globe  v^estward  till  the  moon's  place  comes  to  the 
meridian,  and  the  hours  passed  over  by  the  index  will  show  the 
time  from  noon  when  the  moon  will  be  upon  the  meridian. 

Or,  without  the  globe. 

Find  the  moon's  age  by  the  table,  at  page  176,  which  multiply 
by  81*,  and  cut  off  two  figures  from  the  right  hand  of  the  product, 
the  left-hand  figures  will  be  the  hours ;  the  right-hand  figures 
must  be  multiplied  by  60,  for  minutes. 

Or,  correctly,  thus  : 

Take  the  difference  between  the  sun's  and  moon's  right  ascen- 
sion in  24  hours  ;  then,  as  24  hours  diminished  by  this  difference 
is  to  24  hours,  so  is  the  moon's  right  ascension  at  noon,  diminished 
by  the  sun's,  to  the  time  of  the  moon's  transit. 

Examples.  1.  At  what  hour,  on  the  10th  of  April  1825,  did 
the  moon  pass  over  the  meridian  of  Greenwich  ?  The  moon's 
right  ascension  at  midnight  being  301°  15',  and  her  dechnation  17° 
16'  south. 

Answer.  By  the  Globe. — The  moon  came  to  the  meridian  at  three  quarters  past 
six  in  the  morning.f 

By  the  Table,  page  176. — The  moon's  age  was  23;  this  multiplied  by  81  produces 
1863,  that  is,  18  hours  and  63  over  ;  this  63,  multiplied  by  60,  produces 3780,  which, 


*  For,  the  synodic  revolution  of  the  moon  being  about  29^  days,  we  have  by  the 
rule  of  three,  as  29^  d.  :  24  h,  :  :  1  d.  :  81  h. 

t  The  time  of  the  moon's  rising  and  setting  may  be  found  as  for  a  star  or  a  planet, 
see  Problem  LXXI. ;  but  on  account  of  the  moon's  swift  and  irregular  motion, 
the  solution  will  differ  materially  from  the  truth. 


304 


PROBLEMS  PERFORMED  BY 


Part  III. 


by  rejecting  the  two  right-hand  figures,  leaves  37  minutes  j  so  that,  by  this  method, 
the  moon  came  to  the  meridian  at  37  minutes  past  6  o'clock  in  the  morning. 
By  using  the  JsTautical  Mmanac. 

Sun's  right  ascension  at  noon  10th  April  =  1  h.  15'  V'  6 
Ditto  -  -  -    llthApril  =  l        18    41  6 


Increase  of  motion  in  24  hours 

0 

3  40 

Moon's  right  ascension  at  noon 
Ditto 

10th  April 
11th  April 

=  294° 
=  307<^ 

59'  11'^ 
20'  12" 

Increase  in  24  hours 

12' 

21'    1"  equal  to  49' 

24" ;  hence  49'  24'^  diminished  by  3'  40",  leaves  45'  44"  the  moon's  motion  exceeds 

the  sun's  in  24  hours. 

Moon's  right  ascension  294°  59' -f-  4  =+  19  h.  39'  56" 
Sun's  right  ascension       -       -       -       1      15  1.6 

18      24  54.4 

24h. — 45'  44" :  24h.  :  :  ISh.  24'  :  54''  4,  the  true  time  of  the  moon's  passage  over 
the  meridian  in  the  morning,  agreeing  exactly  with  the  Nautical  Almanac. 

2.  At  what  hour,  on  the  first  of  January,  1826,  will  the  moon 
pass  over  the  meridian  of  Greenwich,  the  moon's  right  ascension 
at  noon  being  187  deg.  46  min.^  and  declination  8  degrees  20  min. 
south  ? 

3.  At  what  hour,  on  the  12th  of  March  1826,  will  the  moon  pass 
over  the  meridian  of  Greenwich,  the  moon's  right  ascension  at  mid- 
night being  36  deg.  11  min.,  and  declination  16  deg,  43  min.  north? 

4.  At  what  hour,  on  the  17th  of  October  1826,  will  the  moon 
pass  over  the  meridian  of  Greenwich,  the  moon's  right  ascension 
at  noon  being  38  deg.  15  min.,  and  declination  16  deg.  15  min. 
north  ? 


PROBLEM  CI. 

The  day  of  the  month,  latitude  of  the  place,  and  time  of  high  water 
at  the  full  and  change  of  the  moon  being  given,  to  find  the  time  of 
high  water  on  the  given  day. 

Rule.  Find  the  time  at  which  the  moon  comes  to  the  merid- 
ian of  the  given  place  by  the  preceding  problem,  to  which  add 


♦  When  the  sun's  right  ascension  is  greater  than  the  moon's,  24  hours  must  be 
added  to  the  moon's  right  ascension  before  you  subtract. 


Chap,  II. 


THE  CELESTIAL  GLOBE. 


305 


the  time  of  high  water  at  the  given  place  at  the  full  and  change 
of  the  moon  (taken  from  the  following  Table),  and  the  sum  will 
show  the  time  of  high  water  in  the  afternoon.  If  the  sum  exceed 
twelve  hours,  subtract  12  hours  and  24  minutes  from  it,  and  the 
remainder  will  show  the  time  of  high  water  in  the  morning ;  but 
if  the  sum  exceed  24  hours,  subtract  24  hours  and  48  minutes 
from  it,  and  the  remainder  will  show  the  time  of  high  water  in 
the  afternoon. 

Or,  by  the  TABLE,  PAGE  176. 

Find  the  moon's  age  by  the  Table,  at  page  176.,  and  take  out 
the  time  from  the  right-hand  column  thereof,  answering  to  the 
moon's  age ;  to  which  add  the  time  of  high  water  at  the  full  and 
change  of  the  moon  (taken  from  the  following  Table),  and  the 
sum  will  show  the  time  of  high  w^ater  in  the  afternoon.  If  the 
sum  exceed  12  hours,  subtract  12  hours  and  24  minutes  from  it, 
and  the  remainder  will  show  the  time  of  high  water  in  the  morn- 
ing; but,  if  the  sum  exceed  24  hours,  subtract  24  hours  and  48 
minutes  from  it,  and  the  remainder  will  show  the  time  of  high 
water  in  the  afternoon. 

Or  thus  : 

Find  the  time  of  the  moon's  coming  to  the  meridian  of  Green- 
wich on  the  given  day,  at  page  VI.  of  the  Nautical  Almanac;  take 
out  the  correction  (from  the  following  Table)  to  correspond  to 
this  time,  and  apply  it  as  the  Table  directs  ;  to  the  result  add  the 
time  of  high  water  at  the  full  and  change  of  the  moon  (taken  from 
the  following  Table),  and  the  sum  will  show  the  time  of  high 
water  in  the  afternoon.  If  the  sum  exceed  12  or  24  hours,  pro- 
ceed as  above. 

Examples.  1.  Required  the  time  of  high  water  at  London 
Bridge  on  the  2d  of  April  1825,  the  moon's  right  ascension  at 
that  time  being  179  deg.  24  min.,  and  her  declination  5  deg.  10 
min.  south? 

Answer.    By  the  Globe. — The  moon  came  to  the  meridian  at  11  h.  15' 

Time  of  high  water  at  the  full  and  change  at  London      -  3  0 

Sum     ....  14  15 

Subtract  from  it   -      -  12  24 

Time  of  high  water  in  the  morning         -      ,      -      -  l  51 


39 


306 


PROBLEMS  PERFORMED  BY 


Part  IIL 


By  the  Table,  page  176.    The  moon's  age  was  15,  the  time  answering  to  which. 


in  the  same  Table,  is  - 
Time  of  high  water  at  the  full  and  change  - 

12  h. 

3 

8' 
0 

Sum         -          _  - 

Subtract  from  it  - 

15 
12 

8 
24 

Time  of  high  water  in  the  morning  - 

2 

44 

By  the  J^autical  Mmanac. — The  moon  came  to  the  meridian  at 
The  time  from  the  right-hand  Table  following,  answering  to  11  ) 
hours,  38  minutes,  is           -  \ 

11  h 
0 

38' 
7 

Sum             -  - 
Time  of  high  water  at  London  at  the  full  and  change 

11 

3 

45 
0 

Sum    .          -         -  - 

Subtract  from  it         -  - 

14 
12 

45 
24 

Time  of  high  water  in  the  morning*  - 

2 

21 

2.  Required  the  time  of  high  water  at  Hull,  on  the  25th  of 
May  1826,  the  moon's  right  ascension  at  noon  being  297°  23',  and 
her  declination  16  deg.  44  min.  south. 

3.  Required  the  time  of  high  water  at  Liverpool,  on  the  22d  of 
June  1826,  the  moon's  right  ascension  at  noon  being  305  deg.  38 
min.,  and  her  declination  14  deg.  14  min.  south. 

4.  Required  the  time  of  high  water  at  Limerick,  on  the  19th 
of  August  1826,  the  moon's  right  ascension  at  noon  being  346  deg. 
40  min.,  and  her  declination  35  min.  south. 

5.  Required  the  time  of  high  water  at  Bristol,  on  the  9th  of 
September  1826,  the  moon's  right  ascension  at  noon  being  262 
deg.  21  min.,  and  her  declination  21  deg.  south. 

6.  Required  the  time  of  high  water  at  Dublin,  on  the  12th  of 
October  1826,  the  moon's  right  ascension  at  noon  being  339  deg. 
33  min.,  and  her  declination  3  deg.  14  min.  south. 


*  Here  are  three  methods  of  performing  the  same  problem,  and  the  results  all 
differ  from  each  other :  the  last  is  the  most  correct :  however,  any  one  of  the 
methods  is  as  correct  as  those  which  are  given  in  books  on  pilotage  and  navigation. 


Chap,  IL 


THE  CELESTIAL  GLOBE. 


307 


A  TABLE 

Of  the  Time  of  High  Water  at  New  and  Full  Moon  at  the 
principal  places  in  the  British  Islands. 


Aberdeen 
Ayr 

Aldborough 
St.  Andrew's 
Arran  Island 
Bamborough 
Banff 

Beachy  Head 
St.  Bee's  Head 
Belfast 

Bembridge  Point 
Berwick 
North  Berwick 
St.  Bride's  Bay 
Bridlington  Bay 
Bridport 
Brighton 
Bristol 

Caithness  Point 

Cantire,  Mull, 

Cape  Clear 

Cork 

Cowes 

Cromartie 

Cromer 

Cullen 

Dartmouth 

Dingle  Bay 

Dover 

Dublin 

Dunbar 

Dunbarton 

Dundee 

Dungarvon 

Dungeness 

Eddystone 

Edinburgh 

Exeter 

Exmouth  Bar 
Falmouth 
Fern  Island 


Oh  45' 
10  3C 
9  40 


10  45 
10  0 


10  30 

11  40 


7 

0 

6 

3 
11 

9 

2 
11 

2 

4 

9 

5 

2  ^ 
10  30 

6  20 
5  30 

3  30 


Fifeness 

Flamborough  Head 

N.  and  S.  Foreland 

Fortrose 

Foulness 

Fowey 

Gal  way 

Fort  George 

Gravesend 

Greenock 

Hartland  Point 

Hartlepool 

Harwich 

Holyhead 

Hull 

Kinsale 

Leiih 

Limerick 

Liverpool 

London 

Milford 

Newcastle 

Orfordness 

Plymouth 

Port  Glasgow 

Portland 

Ramsgate 

Rochester 

Sandwich 

Scarborough 

Sligo 

Southampton 

Stockton 

Swansea 

Tynemouth 

Torbay 

Weymouth 

Whitby 

W^hitehaven 

Yarmouth 


2h  0' 
3  40 

10  20 

11  40 
6  45 
5  40 
3  0 

11  40 
1  30 
11  30 


2  20 

4  30 
11  15 

3  0 

5  15 
3  15 
9  45 

6  0 
ll  30 

7  30 
lO  30 

0  45 
j]  30 
3  45 


c  S 


„  15 

Q  0 


308 


PROBLEMS  PERFORMED  BY 


Part  111. 


PROBLEM  CII. 


To  describe  the  apparent  path  of  any  planet,  of  of  a  comet,  amongst 
the  fixed  stars. 

Rule.  Draw  a  straight  line  o,  o,  to  represent  the  ecliptic,  and 
divide  it  into  any  convenient  number  of  equal  parts.  Set  off 
eight  of  those  equal  parts  northward  and  southward  of  the 
ecliptic,  at  each  end  thereof,  and  draw  lines  as  in  the  figure  Plate 
V. ;  these  will  represent  the  zodiac.  Find  the  planet's  geocentric 
latitude  and  longitude  in  an  ephemeris,or  in  the  Nautical  Almanac, 
and  mark  its  place  for  every  month,  or  for  several  days  in  each 
month,  beginning  at  the  right  hand  of  the  ecliptic  line,  and 
proceeding  towards  the  left.* 

Find  the  latitudes  and  longitudesf  of  the  principal  stars  in  the 
several  constellations  near  which  the  planet  passes,  and  set  them 
off  in  a  similar  manner  from  the  right  hand  towards  the  left;  you 
will  thus  have  a  complete  picture  of  any  part  of  the  heavens, 
with  the  positions  of  the  several  stars,  &c.  as  they  appear  to  a 
spectator  on  the  earth. 

Example.  Delineate  the  path  of  the  planet  Jupiter  for  the 
year  1811  ;  the  latitudes  and  longitudes  being  as  follow. J 


*  The  young  student  will  recollect  that  the  stars  appear  in  a  contrary  order  in 
the  heavens  to  what  they  do  on  the  surface  of  a  globe.  In  the  heavens  we  see  the 
concave  part,  on  the  globe  the  convex.  This  manner  of  delineating  the  stars  will 
be  found  extremely  useful,  and  will  enable  the  student  to  know  their  names  and 
places  sooner  than  by  the  globe. 

t  The  places  of  the  stars  may  likewise  be  laid  down  by  their  right  ascensions  and 
dechnations,  by  drawing  a  portion  of  the  equinoctial  instead  of  the  ecliptic. 

X  As  Jupiter  performs  his  revolution  round  the  sun  in  11  years  315  days  (see 
page  156)  he  will  have  nearly  the  same  longitude  in  the  years  1823  and  1S25, 
consequently  he  will  pass  through  the  same  constellations  as  are  delineated  in 


Chap.  II. 


THE  CELESTIAL  GLOBE. 


309 


Longitudes. 

Jan.  1st  Is  21°  45' 

Feb.  7th  1  22  II 

 25th  I  23  58 

March  1st  1  24  29 

 25th  I  28  16 

April  1st  1  29  35 

:  25th  2    4  30 

May  1st  2    5  49 

 13th  2    8  31 

 25th  2  11  17 

June  1st  2  12  54 

 25th  2  18  27 

July  7th  2  21  49 


Latitudes. 


0°  57'  S. 

July  25th 

0  47 

S. 

Aug.  7th 

0  43 

s. 

19th 

0  42 

s. 

25th 

0  37 

s. 

Sept.  7th 

0  36 

s. 

25th 

0  32 

s. 

Oct.  7th 

0  31 

s. 

25th 

0  30 

s. 

Nov.  1st 

0  29 

s. 

19th 

0  28 

s. 

25th 

0  26 

s. 

Dec.  13th 

0  25 

s. 

25th 

^itudes. 

Latitudes. 

2s25°  r 

0-24'  S. 

2  27  36 

0  23 

S. 

2  29  48 

0  22 

s. 

3 

0  48 

0  22 

s. 

3 

2  45 

0  21 

s. 

3 

4  50 

0  21 

s. 

3 

5  44 

0  20 

s. 

3 

6  15 

0  19 

s. 

3 

6  10 

0  18 

s. 

3 

5  12 

0  17 

s. 

3 

4  40 

0  16 

s. 

3 

2  34 

0  14 

s. 

3 

0  57 

0  12 

s. 

Jupiter's  path,  when  delineated,  will  be  south  of  the  ecliptic  in 
the  order  A,  B,  C,  D,  E,  F,  G,  H.  Thus,  he  will  appear  at  A  on 
the  first  of  January,  at  B  on  the  first  of  March,  at  C  on  the  first 
of  April,  at  D  on  the  first  of  May,  at  E  on  the  first  of  June,  at  F 
on  the  7th  of  July,  at  G  on  the  25  of  August,  and  at  H  on  the 
25th  of  October.  On  the  25th  of  August,  when  Jupiter  appears 
at  G,  he  will  be  a  little  to  the  right  hand  of  the  star  marked  jj  in 
Gemini ;  when  he  arrives  at  H,  which  will  happen  on  the  25th 
of  October,  he  will  apparently  return  again  to  G,  a  small  matter 
above  his  former  path,  where  he  will  be  situated  on  the  25th  of 
December.  Jupiter  will  not  be  visible  during  the  whole  of  his 
apparent  progress  from  A  to  H,  being  too  near  to  the  sun  during 
the  months  of  May  and  June, 

In  the  same  manner  the  places  and  situations  of  the  stars  may 
be  delineated  ;  thus  Aldebaran,  the  principal  star  in  the  Hyades, 
will  be  found  by  the  globe,  (or  a  proper  table)  to  be  situated  in  7° 
of  n  and  in  5|°  of  south  latitude  ;  Betelgeux  in  Orion's  right 
shoulder,  is  about  26°  of  n  and  16°  of  south  latitude,  and  its  place 
may  be  laid  down  on  a  map  by  extending  the  hne  of  its  longitude, 
as  from  L,  till  it  meets  a  straight  line  passing  through  16,  16,  on 
the  sides  of  the  map.  In  the  same  manner  any  other  star's  situ- 
ation may  be  described  ;  thus  the  Hyades  will  appear  at  Q,  the 
Pleiades  at  P,  &:c.  and  Bellatrix,  SfO,.  as  in  the  figure. 

The  constellation  Orion,  here  described,  is  a  very  conspicuous 
object  in  the  heavens  in  the  months  of  January  and  February, 
about  9  or  10  o'clock  in  the  evening,  and  will  be  an  excellent 
guide  for  determining  the  positions  of  several  other  constellations, 
particularly  Canis  Major,  Canis  Minor,  Auriga,  &c.  See  page 
129. 


310 


A  PROMISCUOUS  COLLECTION 


Part  IV. 


PART  IV. 


CONTAINING 

I.  A  promiscuous  Collection  of  Examples  exercising  the  Problems 
on  the  Globes. — 2.  A  collection  of  Questions,  with  References 
to  the  pages  where  the  Answers  will  be  found ;  designed  as  an 
Assistant  to  the  Tutor  in  the  Examination  of  the  Scholar. 

CHAPTER  I. 

A  promiscuous  Collection  of  Examples  exercising  the  Problems 

on  the  Globes. 

1.  What  day  of  the  year  is  of  the  same  length  as  the  14th  of 
August  ? 

2.  How  many  miles  make  a  degree  of  longitude  in  the  latitude 
of  Lisbon  ? 

3.  At  what  hour  is  the  sun  due  east  at  London  on  the  5th  of 
May? 

4.  There  is  a  place  in  the  parallel  of  31  degrees  of  north  lati- 
tude, which  is  31  degrees  distant  from  London  ;  what  place  is  it  ? 

5.  If  the  sun's  meridian  altitude  at  liOndon  be  30  degrees,  what 
day  of  the  month,  and  what  month  is  it  ? 

6.  On  what  month  and  day  is  the  sun's  meridian  altitude  at 
Paris  equal  to  the  latitude  of  Paris  ? 

7.  When  y  Draconis  is  vertical  to  the  inhabitants  of  London 
at  ten  o'clock  at  night ;  what  day  of  the  month,  and  what  month 
is  it? 

8.  What  is  the  equation  of  time  dependent  on  the  obliquity  of 
the  ecliptic  on  the  14th  of  July  ? 

9.  I  observed  the  pointers  in  the  Great  Bear,  on  the  meridian 
of  London,  at  eleven  o'clock  at  night ;  in  what  month,  and  on 
what  night,  did  this  happen  ? 

10.  On  what  day  of  the  month,  and  in  what  month,  will  the 
shadow  of  a  cane  placed  perpendicular  to  the  horizon  of  Lon- 


Chap.  I. 


OF  EXERCISES  ON  THE  GLOBES. 


311 


don,  at  ten  o'clock  in  the  nmorning,  be  exactly  equal  in  length  to 
the  cane  ? 

11.  The  earth  goes  round  the  sun  in  365  days 6  hours  nearly ; 
how  many  degrees  does  it  move  in  one  day,  at  a  medium  ?  Or, 
what  is  the  daily  apparent  mean  motion  of  the  sun  ? 

12.  The  moon  goes  once  round  her  orbit,  from  the  first  point 
of  the  sign  Aries  to  the  same  again,  in  27  days  7  hours  43  min. 
5  seconds :  what  is  her  mean  motion  in  one  day  ? 

13.  The  moon  turns  round  her  axis,  from  the  sun  to  the  sun 
again,  in  29  days  12  hours  44  minutes  3  seconds,  which  is  exactly 
the  time  that  she  takes  to  go  round  her  orbit  from  new  moon  to 
new  moon  ;  at  what  rate  per  hour  are  the  inhabitants  (if  any)  of 
her  equatorial  parts  carried  by  this  rotation,  the  moon's  diameter 
being  2144  miles  ? 

14.  How  many  degrees  does  the  motion  of  the  moon  exceed 
the  apparent  motion  of  the  sun  in  24  hours  ? 

15.  Find  on  what  day,  in  any  given  month,  the  moon  is  eight 
days  old,  and  then  find  her  longitude  for  that  day. 

16.  Travelling  in  an  unknown  latitude  1  found,  by  chance,  an 
old  horizontal  dial  ;  the  hour-lines  of  which  were  so  defaced  by 
time  that  1  could  only  discover  those  of  IV.  and  V.,  and  found 
their  distance  to  be  exactly  21  degrees  ;  pray,  what  latitude  was 
the  dial  made  for  ? 

17.  Required  the  duration  of  twilight  at  the  south  pole. 

18.  How  far  must  an  inhabitant  of  London  travel  southward 
to  lose  sight  of  Aldebaran  ? 

19.  What  is  the  elevation  of  the  north  polar  star  above  the 
horizon  of  Calcutta  ? 

20.  Lord  Nelson  beat  the  French  fleet  near  latitude  21  deg.  11 
min.  north,  longitude  30  deg.  22  min.  east ;  point  out  the  place 
on  the  globe. 

21.  What  is  the  sun's  altitude  at  three  o'clock  in  the  afternoon 
at  Philadelphia  on  the  7th  of  May? 

22.  What  is  the  length  of  the  day  at  London  on  the  26th  of 
July,  and  how  many  degrees  must  the  sun's  declination  be  dimin- 
ished to  make  the  day  an  hour  shorter  ? 

23.  At  what  hour  does  the  sun  first  make  his  appearance  at 
Petersburgh  on  the  4th  of  June  ? 

24.  At  what  rate  per  hour  are  the  inhabitants  of  Botany  Bay 
carried  from  west  to  east  by  the  rotation  of  the  earth  on  its  axis  ? 

25.  When  Arcturus  is  30  degrees  above  the  horizon  of  Lon- 
don, and  eastward  of  the  meridian,  on  the  5th  of  November,  what 
o'clock  is  it  ? 


312 


A  PROMISCUOUS  COLLECTION. 


Part  IV. 


26.  Describe  an  horizontal  dial  for  the  latitude  of  Washington. 

27.  Describe  a  vertical  dial  facing  the  south  for  the  latitude  of 
Edinburgh. 

28.  What  is  the  moon's  greatest  altitude  to  the  inhabitants  of 
Dublin  ? 

29.  What  is  the  sun's  greatest  altitude  at  the  southern  extrem- 
ity of  Patagonia  ? 

30.  At  what  hour  at  London,  on  the  15th  of  August,  will  the 
Pleiades  be  on  the  meridian  of  Philadelphia  ? 

31.  If  a  comet,  whose  longitude  was  4  signs  5  deg.,  and  lati- 
tude 44  deg.  north,  appeared  in  Ursa  Major,  in  what  part  of  the 
constellation  was  it  ? 

32.  On  what  point  of  the  compass  does  the  sun  set  at  Mad- 
rid, when  constant  twilight  begins  at  London  '? 

33.  What  is  the  difference  between  the  duration  of  twilight  at 
Petersburgh  and  Calcutta,  on  the  first  of  February  ? 

34.  How  much  longer  is  the  10th  of  December  at  Madras  than 
at  Archangel  ? 

35.  How  much  longer  is  the  5th  of  May  at  Archangel  than  at 
Madras  ? 

36.  When  it  is  two  o'clock  in  the  afternoon  at  London,  on  the 
15th  of  February,  to  what  places  is  the  sun  rising  and  setting,  and 
where  is  it  noon  ? 

37.  Whether  does  the  sun  shine  over  the  north  or  south  pole 
on  the  17th  of  April,  and  how  far? 

38.  At  what  hour  on  the  18th  of  April  will  the  sun's  altitude 
and  azimuth,  from  the  east  towards  the  south,  be  each  40  degrees 
at  London  ? 

39.  Which  way  must  a  ship  steer  from  Rio  Janeiro  to  the  Cape 
of  Good  Hope? 

40.  Are  the  clocks  at  Philadelphia  faster  or  slower  than  those 
at  London,  and  how  much  ? 

41.  Are  the  clocks  at  Calcutta  faster  or  slower  than  the  clocks 
at  London,  and  how  much  ? 

42.  What  is  the  difference  of  latitude  between  Copenhagen 
and  Venice  ? 

43.  There  is  a  place  in  latitude  31°  IP  north,  situated,  by  an 
angle  of  position,  south-east  by  east  ^  east  from  London  ;  what 
place  is  that,  and  how^  far  is  it  from  London  in  English  miles  ? 

44.  On  the  1st  of  February  1825,  the  longitude  of  Venus  was 
11  signs  25°  41',  latitude  0°  26'  south;  did  Venus  rise  before  or 
after  the  sun,  and  how  much  ? 

45.  On  the  7th  of  September  1825,  the  longitude  of  Venus 


Chap.  L 


OF  EXERCISES  ON  THE  GLOBES. 


313 


will  be  4  signs  2  deg.  44  min.,  latitude  0  deg.  51  min.  south  ;  will 
Venus  rise  before  or  after  the  sun,  and  how  much  ? 

46.  On  the  25th  day  of  December,  1826,  the  longitude  of  the 
planet  Jupiter  will  be  6  signs,  12  deg.  34  min.,  latitude  1  deg.  18 
min.  north ;  at  what  hour  will  he  rise,  come  to  the  meridian,  and 
set,  at  London  ? 

47.  On  the  7th  of  January  1825,  the  moon's  longitude  at  mid- 
night was  5  signs  28  deg.  30  min.,  latitude  4  deg.  28  min.  south  ; 
required  her  rising  amplitude  at  London,  and  the  hour  and  azi- 
muth, when  she  was  30  deg.  above  the  horizon. 

48.  The  moon's  longitude  on  the  5th  of  November  1826,  at 
midnight,  will  be  10  signs,  4  deg.  1  min.,  latitude  4  deg.  59  min. 
north  ;  required  the  time  of  her  rising,  coming  to  the  meridian, 
and  setting,  at  London,  and  the  time  of  high  water  at  London 
Bridge. 

49.  To  what  places  of  the  earth  will  the  moon  be  vertical  on 
the  6th  of  February  1826,  her  longitude  at  midnight  being  10 
signs,  17  deg.  34  min.,  and  latitude  4  deg.  40  min.  north  ? 

50.  On  the  1st  of  March,  1826,  the  moon's  ascending  node 
will  be  8  signs,  7  deg.  14  min.  ;  where  will  the  descending  node 
be? 

51.  The  moon's  declination  at  midnight,  on  the  1st  of  Novem- 
ber 1826,  will  be  20  deg.  15  min.  south ;  to  what  places  of  the 
earth  will  she  be  vertical  ? 

52.  What  stars  are  constantly  above  the  horizon  of  Copenha- 
gen ? 

53.  I  observed  the  altitude  of  Betelgeux  to  be  19  deg.  and  that 
of  Aldebaran  40  deg. ;  they  both  appeared  in  the  same  azimuth, 
viz.  exactly  east ;  what  latitude  w^as  I  in  ? 

54.  In  what  latitude  is  Aldebaran  on  the  meridian  when  &  in 
the  Lion's  tail  is  rising  ? 

55.  In  what  latitude  is  Rigel  setting  when  Regulus  is  on  the 
meridian  ? 

56.  In  what  latitude  are  the  pointers  in  the  Great  Bear  on  the 
meridian  when  Vega  is  rising  1 

57.  In  latitude  79  deg.  north,  on  the  1st  of  February,  at  what 
hour  will  Procyon  and  Regulus  have  the  same  altitude  ? 

58.  At  what  hour  on  the  10th  of  February,  will  Capella  and 
Procyon  have  the  same  azimuth  at  London  ? 

59.  On  the  10th  of  November  at  eight  o'clock  in  the  evening, 
Bellatrix  in  the  left  shoulder  of  Orion  was  rising  :  what  was  the 
latitude  of  the  place  ? 


40 


314 


A  PROMISCUOUS  COLLECTION 


Part  lY. 


60.  On  the  16th  of  February,  Arcturus  rose  at  eight  o'clock  in 
the  evening  ;  what  was  the  latitude  ? 

61.  At  what  hour  of  the  night,  on  the  IGth  of  February,  will 
the  altitude  of  Regulus  be  28  deg.  at  London  ? 

62.  Required  the  altitude  and  azimuth  of  Markab  in  Pegasus, 
at  London,  on  the  21st  of  September,  at  nine  o'clock  in  the  eve- 
ning ? 

63.  On  what  day  of  the  month,  and  in  what  month,  will  the 
pointers  of  the  Great  Bear  be  on  the  meridian  of  London  at  mid- 
night ? 

64.  What  inhabitants  of  the  earth  have  the  greatest  portion  of 
moon-light  ? 

65.  On  what  day  of  the  year  will  Altair,  in  the  Eagle,  come 
to  the  meridian  of  London  with  the  sun  ? 

66.  In  what  latitude  north  is  the  length  of  the  longest  day  11 
times  that  of  the  shortest  ? 

67.  In  what  latitude  south  is  the  longest  day  eighteen  hours  ? 

68.  At  what  time  does  the  morning  twilight  begin,  and  at  what 
lime  does  the  evening  twilight  end,  at  Philadelphia,  on  the  15th 
of  January  ? 

69.  When  it  is  four  o'clock  in  the  afternoon  at  London,  on  the 
4th  of  June,  where  is  it  twilight  ? 

70.  Required  the  antipodes  of  Cape  Horn. 
7L  Required  the  Perioeci  of  Philadelphia. 

72.  Required  the  antoeci  of  the  Sandwich  Islands. 

73.  What  is  the  angle  of  position  between  London  and  Jerusa- 
lem ? 

74.  Required  the  distance  between  London  and  Alexandria, 
in  English  and  in  geographical  miles  ? 

75.  In  what  latitude  north  does  the  sun  begin  to  shine  con- 
stantly on  the  10th  of  April  ? 

76.  How  long  does  the  sun  shine  without  setting  at  the  north 
pole  ;  and  what  is  the  duration  of  dark  night  ? 

77.  Where  is  the  sun  vertical  when  it  is  midnight  at  Dublin  on 
the  15th  of  July  ? 

78.  When  it  is  five  o'clock  in  the  evening  at  Philadelphia, 
where  is  it  midnight,  and  where  is  it  noon  ? 

79.  What  places  have  the  same  hours  of  the  day  as  Edinburgh  ? 

80.  What  places  have  opposite  hours  to  the  respective  capitals 
of  Europe  ? 

81.  At  what  hour  at  London  is  the  sun  due  east  at  the  time  of 
the  equinoxes  ? 


Chap,  1. 


OF  EXERCISES  ON  THE  GLOBES. 


315 


82.  At  what  hour  at  London  is  the  sun  due  east  at  the  time  of 
the  solstices  ? 

83.  In  what  climates  are  the  following  places  situated,  viz. 
Philadelphia,  Madrid,  Drontheim,  Trincomale,  Calcutta,  and 
Astracan  ? 

84.  On  what  day  of  the  year  does  Regulus  rise  heliacally  at 
London  ? 

85.  On  what  day  of  the  year  does  Betelgeux  set  heliacally  at 
London  ? 

86.  What  stars  set  acronically  at  London  on  the  24th  of  De- 
cember ? 

87.  What  stars  rise  acronically  at  London  on  the  12th  of  De- 
cember ? 

88.  In  what  latitude  north  do  the  bright  stars  in  the  head  of  the 
Dolphin,  and  Altair  in  the  Eagle,  rise  at  the  same  hour  ? 

89.  In  what  latitude  north  do  Capella  and  Castor  set  at  the 
same  hour,  and  what  is  the  difference  of  time  between  their  com- 
ing to  the  meridian  ? 

90.  What  stars  rise  cosmically  at  London  on  the  7th  of  De- 
cember ? 

91.  What  stars  set  cosmically  at  London  the  10th  of  Decem- 
ber? 

92.  What  degrees  of  the  ecliptic  and  equinoctial  rise  with 
Aldebaran  at  London  ? 

93.  On  what  day  of  the  year  does  Arcturus  come  to  the  me- 
ridian of  London,  at  two  o'clock  in  the  morning  ? 

94.  On  what  day  of  the  year  does  Regulus  come  to  the  merid- 
ian of  London,  at  nine  o'clock  in  the  evening  ? 

95.  At  what  time  does  Vega  in  Lyra  come  to  the  meridian  of 
London,  on  the  18th  of  August  ? 

96.  Trace  out  the  galaxy  or  milky-way  on  the  celestial  globe. 

97.  If  the  meridian  altitude  of  the  sun  on  the  7th  of  June  be 
50  deg.,  and  south  of  the  observer,  what  is  the  latitude  of  the 
place  ? 

98.  Required  the  sun's  right  and  oblique  ascension  at  London 
at  the  equinoxes. 

99.  Required  the  sun's  right  ascension,  oblique  ascension,  as- 
censional difference,  and  time  of  rising  and  setting  at  London,  on 
the  5th  of  May? 

100.  If  the  sun's  rising  amplitude  on  the  7th  of  June  be  24 
deg.  to  the  northward  of  the  east,  what  is  the  latitude  of  the 
place  ? 

101.  What  stars  have  the  following  degrees  of  right  ascensions 
and  declinations  ? 


316 


A  PROMISCUOUS  COLLECTION. 


Part  IV. 


7°  10'  R.A.  29°  45'  D.N. 
14  38  R.A.  34  33  D.N. 
135  59  R.A.   3  10  D.N. 


162^  49'  R.A.  62^50'  D.N. 
244  17  R.A.  25  28  D.S. 
238  27  R  A.  19  15  D.S. 


102.  Describe  an  horizontal  sun-dial,  for  the  latitude  of  Edin- 
burgh. 

103.  What  is  the  length  of  the  day  on  February  14th  at  Lon- 
don, and  how  much  must  the  sun's  declination  decrease  to  make 
the  day  an  hour  longer  ? 

104.  What  hour  is  it  at  London  when  it  is  17  minutes  past  4 
in  the  evening  at  Jerusalem  ? 

105.  On  the  21st  of  June,  the  sun's  altitude  was  observed  to  be 
46  deg.  25  min.,  and  his  azimuth  112  deg.  59  min.  from  the  north 
towards  the  east,  at  London  ;  what  was  the  hour  of  the  day  ? 

106.  Given  the  sun's  declination  17  deg.  2  min.  north,  and  in- 
creasing ;  to  find  the  sun's  longitude,  right  ascension,  and  the  an- 
gle formed  between  the  ecliptic  and  the  meridian  passing  through 
the  sun. 

107.  Given  the  sun's  right  ascension  225  deg.  18  min.  to' find 
his  longitude,  declination,  and  the  angle  formed  between  the 
ecliptic  and  the  meridian  passing  through  the  sun. 

108.  Given  the  sun's  longitude  26  deg.  9  min.  in  b  ;  to  find 
his  declination,  right  ascension,  and  the  angle  formed  between  the 
ecliptic  and  the  meridian  passing  through  the  sun. 

109.  Given  the  sun's  amplitude  39  deg.  50.  min.  from  the  east 
towards  the  north,  and  his  declination  23^  deg.  north  ;  to  find  the 
latitude  of  the  place,  the  time  of  the  sun's  rising  and  setting,  and 
the  length  of  the  day  and  night. 

110.  At  what  time,  on  the  first  of  April,  will  Arcturus 
appear  upon  the  6  o'clock  hour-line  at  London,  and  what  will  his 
altitude  and  azimuth  be  at  that  time  ? 

111.  Required  the  altitude  of  the  sun,  and  the  hour  he  will  ap- 
pear due  east  at  London,  on  the  20th  of  May. 

112.  At  what  hours  will  Arcturus  appear  due  east  and  west  at 
London,  on  the  2d  of  April,  and  what  will  its  altitude  be  ? 

113.  At  London,  the  suns  altitude  was  observed  to  be  25  deg. 
30  min.  when  on  the  prime  vertical ;  required  his  declination  and 
the  hour  of  the  day. 

114.  On  the  25th  of  April  1826,  the  moon's  right  ascension  at 
midnight  will  be  266  deg.  23  min.,  and  her  declination  21  deg.  18 
min.  south ;  required  her  distance  from  Regulus,  Procyon,  and 
Betelguex,  at  that  time  ? 

115.  The  distance  of  a  comet  from  Sirius  was  observed  to  be 


Chap,  I. 


OP  EXERCISES  ON  THE  GLOBES. 


317 


66  deg.,  and  from  Procyon  51  deg.  6  min. ;  the  comet  was  west- 
ward of  Sirius  :  required  its  latitude  and  longitude. 

116.  Find  the  Golden  Number,  the  Epact,  Sunday  Letter, 
the  Number  of  Direction,  the  Paschal  full  moon,  and  Easter  day, 
for  the  years  1826,  1828,  1835,  and  1840,  distinguishing  the  leap- 
years. 

117.  The  declination  of  y  in  the  head  of  Draco  is  51  deg.  31 
min.  north  ;  to  what  places  will  it  be  vertical  when  it  comes  to 
their  respective  meridians  ? 

118.  When  it  is  four  o'clock  in  the  evening  at  London  on  the 
4th  of  May,  to  what  places  is  the  sun  rising  and  settmg,  where 
is  it  noon  and  midnight,  and  to  what  place  is  the  sun  verical  ? 

119.  At  what  time  does  the  sun  rise  and  set  at  the  North 
Cape,  on  the  North  of  Lapland,  on  the  5th  of  April,  and  what  is 
the  length  of  the  day  and  night  ? 

120.  At  what  time  does  the  sun  rise  at  the  Shetland  Islands 
when  it  sets  at  four  o'clock  in  the  afternoon  at  Cape  Horn  ? 

121.  Walking  in  Kensington  Gardens  on  the  17th  of  May,  it 
was  twelve  o'clock  by  the  sun-dial,  and  wanted  eight  minutes  to 
twelve  by  my  watch  ;  was  my  watch  right? 

122.  If  the  sun  set  at  nine  o'clock,  at  what  time  does  it  rise, 
and  what  is  the  length  of  the  day  and  night? 

123.  Where  is  the  sun  vertical  when  it  is  five  o'clock  in  the 
morning  at  London  on  the  15th  of  May  ? 

124.  At  what  hour  does  day  break  at.  London  on  the  5th  of 
April  ? 

125.  If  the  moon  be  five  days  old  on  the  9th  of  June  1826,  at 
what  time  does  she  rise,  culminate,  and  set,  at  London  ? 

126.  On  what  day  of  the  month,  and  in  what  month,  does  the 
sun  rise  24  deg.  to  the  north  of  the  east  at  London  ? 

127.  When  the  sun  is  rising  to  the  inhabitants  of  London  on 
the  8th  of  May,  where  is  it  setting  ? 

128.  When  the  sun  is  setting  to  the  inhabitants  of  Calcutta,  on 
the  18th  of  March,  where  is  it  midnight? 

129.  What  is  the  difference  between  the  circumference  of  the 
earth  at  the  equator  and  at  Petersburgh,  in  English  miles  ? 

130.  At  what  hour  does  the  sun  rise  at  Barbadoes  when  con- 
stant twilight  begins  at  Dublin  ? 

131.  When  the  sun  is  rising  at  Owhyhee  on  the  18th  of  May, 
where  is  it  noon  ? 

132.  At  what  hour  does  the  sun  rise  at  London  when  it  sets  at 
seven  o'clock  at  Petersburg  ? 


318 


A  PROMISCUOUS  COLLECTION. 


Part  IV. 


133.  How  high  is  the  north  polar  star  above  the  horizon  of 
Quebec  ? 

134.  How  many  EngUsh  miles  must  an  inhabitant  of  London 
travel  southward,  that  the  meridian  altitude  of  the  north  polar 
star  may  be  diminished  25  degrees  ? 

135.  How  many  English  miles  must  I  sail  or  travel  westward 
from  London  that  my  watch  may  be  seven  hours  too  fast  ? 

136.  What  place  of  the  earth  has  the  sun  in  the  zenith,  when 
it  is  seven  o'clock  in  the  morning  at  London,  on  the  25th  of 
April  ? 

137.  On  what  day  of  the  month,  and  in  what  month,  is  the 
sun's  amplitude  at  London  equal  to  one-third  of  the  latitude  ? 

138.  On  what  month  and  day  is  the  sun's  amplitude  at  London 
equal  to  the  latitude  of  Kingston,  in  Jamaica? 

139.  If  the  moon  be  three  days  old  on  the  10th  of  March  1826, 
w^hat  is  her  longitude  ? 

140.  If  the  highest  point  of  Mont  Blanc  be  5101  yards  above 
the  level  of  the  sea,  what  would  be  its  altitude  on  a  globe  of  18 
inches  in  diameter? 

141.  If  the  polar  diameter  of  the  earth  be  to  the  equatorial 
diameter  as  229  is  to  230,  what  would  the  polar  diameter  of  a 
three-inch  globe  be,  if  constructed  on  this  principle  ? 

142.  What  inhabitants  of  the  earth,  in  the  course  of  12  hours, 
will  be  in  the  same  situation  as  their  antipodes  ? 

143.  On  what  day  of  the  year  at  London  is  the  twilight  eight 
hours  long  ? 

144.  At  what  time  does  the  sun  rise  and  set  at  London  when 
the  inhabitants  of  the  north  pole  begin  to  have  dark  night  ? 

145.  At  what  hour  does  the  sun  set  at  the  Cape  of  Good  Hope, 
when  total  darkness  ends  at  the  north  pole  ? 

146.  What  is  the  moon's  longitude  if  full  moon  happens  on  the 
2d  of  April  1825  ? 

147.  Does  the  sun  ever  rise  and  set  at  the  north  pole  ? 

148.  At  what  hour  of  the  day,  on  the  15th  of  April,  will  a 
person  at  London  have  his  shadow  the  shortest  possible  ? 

149.  If  the  precession  of  the  equinoxes  be  50^  seconds  in  a 
year,  how  many  years  will  elapse  before  the  constellation  Aries 
will  coincide  with  the  solstitial  colure  ? 

150.  If  the  obliquity  of  the  ecliptic  be  continually  diminishing 
at  the  rate  of  56  seconds  in  a  century,  as  stated  by  several  authors, 
how  many  years  will  elapse  from  the  1st  of  January  1825,  when 
the  obliquity  of  the  ecliptic  was  23  degrees  27  minutes  44  seconds, 
before  the  ecliptic  will  coincide  with  the  equinoctial  ? 


Chap.  I. 


OF  EXERCISES  ON  THE  GLOBES. 


319 


151.  Required  the  duration  of  dark  night  at  the  south  of  Nova 
Zembla. 

152.  When  constant  twilight  ends  at  Petersburgh,  where  is  the 
day  18  hours  long  ? 

153.  At  what  hour  does  the  sun  set  at  Constantinople,  when  it 
rises  12  degrees  to  the  north  of  the  east  ? 

154.  What  is  the  difference  between  a  solar  and  a  siderial 
year,  and  what  does  that  difference  arise  from  ? 

155.  What  is  the  difference  between  the  length  of  a  natural  or 
astronomical  day  and  a  siderial  day,  and  how  does  the  difference 
arise  ? 

156.  Required  the  difference  between  the  length  of  the  longest 
day  at  Cape  Horn  and  at  Edinburgh. 

157.  If  one  man  were  to  travel  eight  miles  a  day  westward 
round  the  earth  at  the  equator,  and  another  two  miles  a  day 
westward  round  it  in  the  latitude  of  80  degrees  north ;  in  how 
many  days  would  each  of  them  return  to  the  place  whence  he 
set  out  ? 

158.  If  a  pole  of  18  feet  in  length  be  placed  perpendicular  to 
the  horizon  of  London  on  the  15th  of  July,  and  another  exactly 
of  the  same  length  be  placed  in  a  similar  manner  at  Edinburgh, 
which  will  cast  the  longer  shadow  at  noon  ? 

159.  If  the  moon  be  in  29  degrees  of  Leo  at  the  time  of  new 
moon,  what  sign  and  degree  will  she  be  in  when  she  is  five  days 
old? 

160.  What  is  the  duration  of  constant  day  or  twilight  at  the 
north  of  Spitzbergen  ? 

161.  What  place  upon  the  globe  has  the  greatest  longitude,  the 
least  longitude,  no  longitude,  and  every  longitude  ? 

162.  In  what  latitude  is  the  length  of  the  longest  day,  to  the 
length  of  the  shortest,  in  the  ratio  of  3  to  2  ? 

163.  If  a  man  of  six  feet  high  were  to  travel  round  the  earth, 
how  much  farther  would  his  head  go  than  his  feet  ? 

164.  On  what  day  of  the  week  will  the  tenth  of  January  fall 
in  the  year  1835  ? 

165.  At  what  hour,  in  the  afternoon,  London  time,  on  the  21st 
of  June,  will  the  shadow  of  a  pole  ten  feet  high  at  Barbadoes,  be 
of  the  same  length  as  the  meridional  shadow  of  a  similar  pole  at 
London  on  the  same  day  ? 

166.  One  end  of  a  wall  declines  30  degrees  from  the  east 
towards  the  north,  and  the  other  end  60  deg.  from  the  south 
towards  the  west  in  latitude  51°  30'  N. ;  at  what  hour  on  the  21st 


320  QUESTIONS  FOR  THE  EXAMINATION  OF  PartlY, 

of  June  does  the  sun  begin  to  shine  on  the  south  of  the  wall,  and 
at  what  hour  does  it  leave  it  ? 

167.  The  south  wall  of  a  church  declines  12  deg.  30  min. 
towards  the  east,  in  latitude  52  deg.  N.,  against  which  a  vertical 
dial  is  fixed  ;  for  how  many  hours  will  the  sun  shine  upon  that 
dial  on  the  tenth  of  May? 

168.  A  clock,  with  a  pendulum  that  beat  seconds,  and  kept 
true  time  on  the  surface  of  the  earth,  was  carried  to  the  top  of  a 
mountain,  and  there  lost  3  seconds  in  an  hour ;  what  was  the 
height  of  the  mountain  ? 


CHAPTER  II. 


A  Collection  of  Questions,  with  References  to  the  Pages  where 
the  Answers  will  be  found ;  designed  as  an  Assistant  to  the 
Tutor^  in  the  examination  of  the  Student. 

1.  How  many  kinds  of  artificial  globes  are  there  ? 

2.  What  does  the  surface  of  the  terrestrial  globe  represent, 
and  which  way  is  its  diurnal  motion?  page  1. 

3.  What  does  the  surface  of  the  celestial  globe  exhibit,  which 
way  is  its  diurnal  motion,  and  where  is  the  student  supposed  to 
be  situated  when  using  it  ? 


*  Though  a  reference  be  given  to  the  pages  where  the  answers  to  each  question 
may  be  found  ;  yet,  perhaps,  it  would  be  better  for  the  student  not  to  learn  the 
answers  by  heart,  verbatim  from  the  book  ;  but  to  frame  an  answer  himself,  from 
an  attentive  perusal  of  his  lesson  :  by  which  means  the  understanding  will  be 
called  into  exercise  as  well  as  the  memory. 


Chap,  11. 


OF  THE  STUDENT. 


321 


I.   GREAT  CIRCLES  ON  THE  TERRESTRIAL  GLOBE. 

1.  What  is  a  great  circle,  and  how  many  are  there  drawn 
on  the  terrestrial  globe  ?  Definition  6,  page  26. 

2.  What  is  the  equator,  and  what  is  its  use?  Def.  10,  page 
26. 

3.  What  are  the  meridians,  and  how  many  are  drawn  on  the 
terrestrial  globe  ?  Def.  8,  page  26. 

4.  What  is  the  first  meridian  ?  Def.  9,  page  26. 

5.  What  is  the  ecliptic,  and  where  is  it  situated?  Def.  11, 
page  27. 

6.  What  are  the  colures,  and  in  how  many  parts  do  they  di- 
vide the  ecliptic  ?  Def  14,  page  28. 

7.  What  are  the  hour-circles,  and  how  are  they  drawn  on  the 
globe?  Def.  50,  page  34. 

8.  What  hour-circle  is  called  the  six  o'clock  hour  line?  Def 
51,  page  35. 

9.  What  are  the  azimuth  or  vertical  circles,  and  what  is  their 
use?  De/".  43,  page  33. 

10.  What  is  the  prime  vertical  ?  Def  44,  page  34. 


II.  small  circles  on  the  terrestrial  globe. 

1.  What  is  a  small  circle,  and  how  many  are  generally 
drawn  on  the  terrestrial  globe  ?  Def.  7,  page  26. 

2.  What  are  the  tropics,  and  how  far  do  they  extend  from  the 
equator,  &c.  ?  Def  16,  page  29. 

3.  What  are  the  polar  circles,  and  where  are  they  situated  ? 
Def  17,  page  29. 

4.  What  are  the  parallels  of  latitude,  and  how  many  are  gen- 
erally drawn  on  the  terrestrial  globe  ?  Def.  18,  page  29. 

5.  What  circles  are  called  Almacanters  ?  Def.  40,  page  33. 


III.  great  circles  on  the  celestial  globe. 

1.  How  many  great  circles  are  drawn  on  the  celestial 
globe  ? 

2.  The  lines  of  terrestrial  longitude  are  perpendicular  to  the 
equator,  on  the  terrestrial  globe,  and  all  meet  in  the  poles  of  the 

41 


322 


QUESTIONS  FOR  THE  EXAMINATION. 


Part  IV. 


world ;  to  what  great  circle  on  the  globe  are  the  lines  of  celestial 
longitude  perpendicular,  and  on  what  points  of  the  globe  do  they 
all  meet. 

3.  What  are  the  colures,  and  into  how  many  parts  do  they 
divide  the  ecliptic  ?  Def.  14,  page  28. 

4.  What  is  the  equinoctial,  and  what  is  its  use  ?  Def.  10,  page 
27. 

5.  What  is  the  ecliptic,  and  where  is  it  situated?  Def.  11, 
page  27. 

6.  What  is  the  zodiac,  and  into  how  many  parts  is  it  divided  ? 
Def.  12,  page  27. 

7.  What  are  the  signs  of  the  zodiac,  and  how  are  they  marked? 
Def.  13,  page  28. 

8.  What  are  the  spring,  summer,  autumnal,  and  winter  signs ; 
and  on  what  days  does  the  sun  enter  them  ?  Def.  13,  page  28. 

9.  What  are  the  ascending  and  descending  signs  ?  Def.  13, 
page  28. 

IV.   SMALL  CIRCLES  ON  THE  CELESTIAL  GLOBE. 

1.  How  many  small  circles  are  drawn  on  the  celestial 
globe  ? 

2.  What  are  the  tropics,  and  how  far  do  they  extend  from  the 
equinoctial?  Def.  16,  page  6. 

3.  What  are  the  polar  circles,  and  where  are  they  situated  ? 
Bef.  17,  page  29. 

4.  What  are  the  parallels  of  celestial  latitude  ?  Def.  41,  page 
33. 

5.  What  are  the  parallels  of  declination  ?  Def.  42,  page  33. 


V.    THE  BRASS  MERIDIAN,  AND  OTHER  APPENDAGES  TO  THE 

GLOBES. 

1.  What  is  the  brazen  meridian,  and  how  is  it  divided  and 
numbered  ?  Def.  5,  page  26. 

2.  What  is  the  axis  of  the  earth,  and  how  is  it  represented  by 
the  artificial  globes  ?  Def.  3,  page  25. 

3.  What  are  the  poles  of  the  world  ?  Def  4,  page  26. 

4.  What  are  the  hour-circles,  and  how  are  they  divided?  Def. 
19,  page  29. 

5.  What  is  the  horizon,  and  what  is  the  distinction  between 


Chap,  II.  OF  THE  STUDENT.  323 

the  rational  and  sensible  horizon?  Defs.  20,  21,  and  22,  pages 
29  and  30. 

6.  What  is  the  wooden  horizon,  and  how  is  it  divided?  Def. 
23,  page  30. 

7.  What  is  the  mariner's  compass,  how  is  it  divided,  and  what 
is  the  use  made  of  it  on  the  globe  ?  Defs.  33,  34,  and  note  page 
33. 

8.  What  is  the  quadrant  of  altitude,  how  is  it  divided,  and  what 
is  its  use  ?    Def.  37,  page  33. 


VI.   POINTS  ON,  AND  BELONGING  TO,  THE  GLOBES. 

1.  What  is  the  pole  of  a  circle  ?    Def  29,  page  31. 

2.  What  is  the  zenith,  and  of  what  circle  is  it  the  pole  ?  Def 

27,  page  31. 

3.  What  is  the  nadir,  and  of  what  circle  is  it  the  pole  ?  Def 

28,  page  31. 

4.  Where  are  the  cardinal  points  of  the  horizon  ?  Def.  24, 
page  31. 

5.  What  are  the  cardinal  points  in  the  heavens  1  Def  25,  page 
31. 

6.  What  are  the  cardinal  points  of  the  ecliptic,  and  which  are 
the  cardinal  signs?  Def.  26,  page  31. 

7.  What  are  the  equinoctial  points?  Def.  30,  p^ige  31. 

8.  What  are  the  solstitial  points?  Def.  31,  page  31. 

9.  What  is  the  culminating  point  of  a  star,  or  of  a  planet  ?  Def. 
52,  page  35. 

10.  What  are  the  poles  of  the  ecliptic,  how  far  are  they  from 
the  poles  of  the  world,  and  in  what  circles  are  thev  situated  ? 
Def  29,  page  31. 

VII.  LATITUDE  AND  LONGITUDE  ON  THE  TERRESTRIAL  GLOBE, 
THE  DIVISION  OF  THE  GLOBE  INTO  ZONES  AND  CLIMATES,  THE 
POSITIONS  OF  THE  SPHERE,  THE  SHADOWS,  AND  POSITIONS  OP 
THE  INHABITANTS  WITH  RESPECT  TO  EACH  OTHER. 

1.  What  is  the  latitude  of  a  place  on  the  terrestrial  globe  ? 
Def  35,  page  32. 

2.  What  is  the  longitude  of  a  place  on  the  terrestrial  globe  ? 
Def  38,  page  33. 

3.  What  is  a  zone,  and  how  many  are  there  on  the  terrestrial 
globe  ?  Def  70,  page  40. 


324 


QUESTIONS  FOR  THE  EXAMINATION 


Part  IV. 


4.  What  is  the  situation,  and  what  is  the  extent  of  the  torrid 
zone?  Def.  71,  page 40. 

5.  Where  are  the  two  temperate  zones  situated,  and  what  is 
the  extent  of  each  ?  Def.  72,  page  40. 

6.  Where  are  the  two  frigid  zones  situated,  and  what  is  the 
extent  of  each  ?  Def.  73,  page  41. 

7.  What  is  a  climate,  and  how  many  are  there  on  the  globe  ? 
De/.  69,  page  38. 

8.  Have  all  places  in  the  same  climate  the  same  atmospherical 
temperature  ?  Note,  page  38. 

9.  How  many  different  positions  of  the  sphere  are  there  ?  Def, 
65,  page  38. 

10.  What  is  a  right  sphere,  and  what  inhabitants  of  the  globe 
have  this  position  ?  Def  66,  page  38  ;  see  likewise  Prob.  XXII. 
page  205. 

11.  What  is  a  parallel  sphere,  and  what  inhabitants  of  the 
globe  have  this  position  ?  Def  67,  page  38 ;  and  Proh.  XXII. 
page  206,  &c. 

12.  What  is  an  oblique  sphere,  and  what  inhabitants  of  the 
globe  have  this  position  ?  Def  68,  page  38 ;  and  Proh.  XXII. 
page  207, 

13.  What  parts  of  the  globe  do  the  Amphiscii  inhabit,  and  why- 
are  they  so  called  ?  Def.  74,  page  41. 

14.  'When  do  the  Amphiscii  obtain  the  name  of  Ascii  ? 

15.  What  parts  of  the  globe  do  the  Heteroscii  inhabit,  and 
why  are  they  so  called  ?  Def  75,  page  41. 

16.  What  parts  of  the  globe  do  the  Periscii  inhabit,  and  why 
are  they  so  called  ?  Def  76,  page  41. 

17.  What  inhabitants  are  called  Antoeci  to  each  other,  and 
what  do  you  observe  with  respect  to  their  latitudes,  longitudes, 
hours,  &c.  ?  Def  77,  page  41. 

18.  What  inhabitants  are  called  Perioeci  to  each  other,  and 
what  is  observed  with  respect  to  their  latitudes,  longitudes,  hours, 
seasons,  &c.  ?  Def  78,  page  41. 

19.  Where  are  the  Antipodes,  and  what  is  observed  with 
respect  to  their  seasons  of  the  year,  &c.  ?  Def  79 j  page  41. 


Chap,  II. 


OP  THE  STUDENT. 


325 


VIII.  LATITUDES  AND  LONGITUDES  OP  THE  STARS  AND  PLANETS 
ON  THE  CELESTIAL  GLOBE,  (fec.  TOGETHER  WITH  THE  POETICAL 
RISING  AND  SETTING  OF  THE  STARS,  &C. 

1.  What  is  the  latitude  of  a  star  or  planet?  Def.  36,  page  33. 

2.  What  is  the  longitude  of  a  star  or  planet  ?  Def.  39,  page  33. 

3.  What  are  the  fixed  stars,  and  why  are  they  so  called?  Def. 
89,  page  45. 

4  What  is  a  constellation,  and  how  many  are  there  on  the 
celestial  globe  ?  Def.  91,  page  46 ;  see  the  tables,  pages  46,  47, 
and  48. 

5.  What  is  meant  by  the  poetical  rising  and  setting  of  the  stars  ? 
Def.  90,  page  45. 

6.  When  is  a  star  said  to  rise  and  set  cosmically  ? 

7.  When  is  a  star  said  to  rise  and  set  acronically  ? 

8.  When  is  a  star  said  to  rise  and  set  heliacally  ? 

9.  What  is  the  Via  Lactea,  and  through  what  constellation 
does  it  pass  ?  Def  92,  page  53. 

10.  What  kind  of  stars  are  termed  nebulous  ?  Def  93,  page 
54. 

11.  How  are  the  stars,  which  have  not  particular  names,  dis- 
tinguished on  the  celestial  globe  ?  Def.  94,  page  54. 


IX.   DEFINITIONS  AND  TERMS  COMMON  TO  BOTH  THE  GLOBES. 


1.  What  is  the  declination  of  the  sun  or  star,  or  planet  ?  Def. 
15,  page  28. 

2.  What  is  an  hemisphere  ?  Def.  32,  page  32. 

3.  What  is  the  altitude  of  any  object  in  the  heavens  ?  Def.  45, 
page  34. 

4.  What  is  the  meridian  altitude  of  the  sun,  a  star,  or  planet  ? 
-  5.  What  is  the  zenith  distance  of  a  celestial  object  ?   Def.  46, 

page  34. 

6.  What  is  the  polar  distance  of  a  celestial  object  ?  Def.  47, 
page  34. 

7.  What  is  the  amplitude  of  a  celestial  object  ?  Def  48,  page 
34. 

8.  What  is  the  azimuth  of  a  celestial  object  ?  Def.  49,  page 
34. 


326  QUESTIONS  FOR  THE  EXAMINATION  Part  IV. 

9.  What  is  the  right  ascension  of  the  sun,  or  of  a  star,  &c.  1 
Bef.  80,  page  41. 

10.  What  is  the  obhque  ascension  of  the  sun,  or  of  a  star,  &c.? 
Def.  81,  page  42. 

11.  What  is  the  oblique  descension  of  the  sun,  or  of  a  star,  &c.? 
Def.  82,  page  42. 

12.  What  is  the  ascensional  or  descensional  difference  ?  Def, 
83,  page  42. 


X.  TIME  ;  YEARS,  DAYS,  &C. 

1.  What  is  a  solar  or  tropical  year,  and  what  is  the  length  of 
it?  Def  62,  page  37. 

2.  What  is  a  siderial  year,  and  what  is  its  duration  ?  Def.  63, 
page  37. 

3.  What  is  an  astronomical  day?  Def.  58,  page  36. 

4.  What  is  a  mean  solar  day  ?  Def  57,  page  35. 

5.  What  is  a  true  solar  day  ?  Def.  56,  page  35. 

6.  What  is  an  artificial  day?  Def.  59,  page  36. 

7.  What  is  a  civil  day  ?  Def.  60,  page  36. 

8.  What  is  a  siderial  day?  Def.  61,  page  36. 

9.  What  is  meant  by  apparent  noon,  or  apparent  time  ?  Def 
53,  page  35. 

10.  What  is  true  or  mean  noon  ?  Def.  54,  page  35. 

11.  What  is  the  equation  of  time  at  noon?  Def.  55,  page  35. 

12.  What  is  the  calendar?  page  171. 

13.  What  is  the  cycle  of  the  moon,  and  how  is  it  found  ?  page 
171. 

14.  What  is  the  epact,  what  is  its  use,  and  how  is  it  found  ? 
page  171. 

15.  What  is  the  cycle  of  the  sun,  how  is  it  found,  and  to  what 
use  is  it  apphed  ?  page  172. 

16.  What  is  the  number  of  direction,  and  how  is  Easter  found 
by  it?  page  173. 

17.  How  do  you  find  the  Paschal  full  moon  and  Easter  by  the 
Epact?  page  174. 

18.  In  how  many  years  will  the  error  in  the  Gregorian  calen- 
dar amount  to  one  day  ?  page  177. 

19.  In  what  manner  do  you  find  the  moon's  age,  the  time  of 
new  moon,  and  the  time  of  full  moon,  by  the  table  page  176. 


Chap.  IL 


OP  THE  STUDENT. 


327 


XI.  ASTRONOMICAL  AND  MISCELLANEOUS  DEFINITIONS,  &;C. 

1.  What  do  you  understand  by  the  precession  of  the  equinoxes, 
and  in  what  time  do  they  make  an  entire  revolution  around  the 
equinoctial  ?  Def.  64,  page  37. 

2.  What  is  the  crepusculum  or  twilight,  and  what  is  the  cause 
of  it?  Def.  84,  page  42. 

3.  What  is  refraction,  and  whence  does  it  arise  ?  Def.  85, 
pages  42,  43  and  44. 

4.  What  is  meant  by  the  parallax  of  the  celestial  bodies  1  Def 
86,  page  44. 

5.  What  is  an  angle  of  position  between  two  places  ?  Def  87, 
page  44  ;  and  note,  pages  199  and  200. 

6.  What  are  rhumbs  and  rhumb-lines  ?  Def.  88,  page  45. 

7.  What  are  the  planets,  and  how  many  belong  to  the  solar 
system  ?  Def  95,  page  55. 

8.  What  is  the  distinction  between  primary  and  secondary 
planets,  and  how  many  secondary  planets  belong  to  the  solar  sys- 
tem ?  Defs.  96,  and  97,  page  55. 

9.  What  is  the  orbit  of  a  planet  ?  Def  98,  page  55.  Of  what 
figure  are  the  orbits  of  the  planets,  and  in  what  part  of  the  figure 
is  the  sun  placed?  page  143. 

10.  What  are  the  nodes  of  a  planet  ?    Def  99,  page  56. 

1 1.  What  are  the  different  aspects  of  the  planets,  and  how  many 
are  there  ?  Def.  100,  page  56. 

12.  What  are  the  syzygies  and  quadratures  of  the  moon  ? 

13.  When  is  a  planet's  motion  said  to  be  direct,  stationary,  or 
retrograde?  Defs.  101,  102,  and  103,  page  56. 

14  What  is  a  digit  ?  Def  104,  page  56. 

15.  What  is  the  disc  of  the  sun  or  moon  ?  Def.  105,  page  56. 

16.  What  are  the  geocentric  and  heliocentric  latitudes  and  lon- 
gitudes of  the  planets  ?  Defs.  106  and  107,  page  56. 

17.  When  is  a  planet  said  to  be  in  apogee  ?  Def  108,  page  56. 

18.  When  is  a  planet  said  to  be  in  perigee  ?  Def.  109,  page  56. 

19.  What  is  the  aphelion  or  higher  apsis  of  a  planet's  orbit  ? 
Def  110,  page  56. 

20.  What  is  the  perihelion  or  lower  apsis  of  a  planet's  orbit  ? 
Def.  Ill,  page  57. 

21.  What  is  the  line  of  the  apsides?  Def  112,  page  57. 


328 


QUESTIONS  FOR  THE  EXAMINATION 


Part  IV. 


22.  What  is  the  eccentricity  of  the  orbit  of  a  planet  ?  Def.  113, 
page  57. 

23.  What  is  the  elongation  of  a  planet?  Def.  118,  page  57. 

24.  What  are  the  occultation  and  transit  of  a  planet  ?  Defs. 
114  and  115,  page  57. 

25.  What  is  the  cause  of  an  eclipse  of  the  sun?  Def.  116, 
page  57. 

26.  What  is  the  cause  of  an  eclipse  of  the  moon  ?  Bef  117, 
page  57. 

27.  What  are  the  nocturnal  and  diurnal  arcs  described  by  the 
heavenly  bodies?  Defs.  119,  and  120,  page  57. 

28.  What  is  the  aberration  of  a  star  ?  Def.  112,  page  57. 

29.  What  are  the  centripetal  and  centrifugal  forces  ?  Defs. 
122  and  123,  page  58. 

30.  What  is  gravity  ?  Def  8,  page  63. 

31.  What  is  the  vis  inertiae  of  a  body  ?  Def  9,  page  63. 

32.  What  is  matter,  and  what  are  its  general  properties  ?  Defs. 
1  and  2,  page  62. 

33.  What  are  extension,  figure,  and  solidity  ?  Defs.  3, 4,  and  5, 
page  62. 

34.  Can  matter  be  divided  ad  infinitum  ?  Def  7,  page  60. 

35.  What  is  motion,  and  what  is  the  distinction  between  abso- 
lute and  relative  motion  ?  Def.  6,  page  62,  and  Def.  10,  page  63. 

36.  How  is  the  velocity  of  a  body  measured,  and  what  do  you 
understand  by  the  word  force  ?  Defs.  11  and  12,  page  64. 

37.  What  are  Sir  I.  Newton's  three  laws  of  motion  ?  pages  64 
and  65. 

38.  What  is  compound  motion  ?  page  65. 


XII.  THE  SOLAR  SYSTEM  AND  THE  SUN, 

1.  What  is  the  solar  system,  and  why  is  it  so  called  ?  page  139. 

2.  What  part  of  the  solar  system  is  called  the  centre  of  the 
world  ?  page  140. 

3.  Does  not  the  sun  revolve  on  its  axis,  and  what  other  motion 
has  it  ?  page  140. 

4.  Of  what  shape  is  the  sun,  how  far  is  it  from  the  earth,  and 
how  many  miles  is  it  in  diameter  ?  pages  140  and  141. 


Chap.  II. 


OF  THE  STUDENT. 


329 


5.  What  is  the  comparative  magnitudes  of  the  sun  and  the 
earth  ?  page  141. 

XIII.  OP  MERCURY,  ^. 

1.  What  is  the  length  of  Mercury's  year?  page  142. 

2.  What  is  the  greatest  elongation  of  Mercury  ? 

3.  What  is  the  distance  of  Mercury  from  the  sun  ? 

4.  What  is  the  diameter  of  Mercury  ?  page  142. 

5.  What  is  the  comparative  magnitudes  of  Mercury  and  the 
earth  ? 

6.  What  is  the  comparison  between  the  light  and  heat  which 
Mercury  receives  from  the  sun,  and  the  light  and  heat  which  the 
earth  receives  ?  page  143. 

7.  At  what  rate  per  hour  are  the  inhabitants  of  Mercury  (if 
any)  carried  round  the  sun  ?  page  143. 

XIV.   OF  VENUS  5. 

1.  When  is  Venus  an  evening  star,  and  in  what  situation  is  she 
a  morning  star  ?  page  144. 

2.  How  long  is  Venus  a  morning  star  ? 

3.  In  how  many  days  does  Venus  revolve  around  the  sun  ? 

4.  The  last  transit  of  Venus  over  the  sun's  disc  happened  in 
1769,  w^hen  will  the  next  transit  happen  ? 

5.  What  is  the  opinion  of  Dr.  Herschel  respecting  the  moun- 
tains in  Venus  ?  page  145. 

6.  What  is  the  opinion  of  M.  Schroeter  on  the  same  subject  ? 
page  152  in  the  note. 

7.  What  is  the  greatest  elongation  of  Venus  ?  page  145. 

8.  What  is  the  diameter  of  Venus  ? 

9.  What  is  the  magnitude  of  Venus  ? 

10.  What  is  the  distance  of  Venus  from  the  sun  ? 

11.  What  is  the  comparison  between  the  light  and  heat  which 
Venus  receives  from  the  sun,  and  the  light  and  heat  which  the 
earth  receives  ? 

12.  At  what  rate  per  hour  does  Venus  move  around  the  sun? 
page  145. 


42 


330 


QUESTIONS  FOR  THE  EXAMINATION  PartW. 


XV.  OF  THE  EARTH,  ©. 

1.  What  is  the  figure  of  the  earth  ?  page  70. 

2.  Why  is  the  earth  represented  by  a  globe  ?  page  76. 

3.  What  proofs  have  we  that  the  earth  is  globular?  pages 
71,  72. 

4.  What  would  be  the  elevation  of  Cbimbora^o,  the  highest 
of  the  Andes  niountains,  on  an  artificial  globe  of  18  inches  diam- 
eter ?  page  72,  the  note. 

5.  What  is  a  spheroid,  and  how  is  it  generated  ?  page  73,  the 
note. 

6.  What  is  the  difference  between  the  polar  and  equatorial 
diameters  of  the  earth  ?  page  74,  and  the  note. 

7.  What  is  the  length  of  a  degree  ?  pages  75,  76,  and  the  note. 

8.  What  is  the  use  of  finding  the  length  of  a  degree,  and  how 
can  the  magnitude  of  the  earth  be  determined  thereby  ?  page  75. 

9.  Who  was  the  first  person  who  measured  the  length  of  a  de- 
gree tolerably  accurate  f  page  75. 

10.  What  is  the  length  of  a  degree  according  to  the  French 
admeasurement  ?  page  76,  the  note. 

11.  In  what  time  does  the  earth  revolve  on  its  axis  from  west 
to  east  ?  page  77,  and  Def.  61,  page  36,  and  the  note. 

12.  What  is  the  diameter  of  the  earth  ;  what  is  its  circumfer- 
ence, and  how  are  they  determined?  page  76,  and  the  note. 

13.  What  proofs  can  you  give  of  the  diurnal  motion  of  the 
earth  ?  pages  77,  and  78. 

14.  How  do  you  explain  the  phenomena  of  the  apparent  diur- 
nal motion  of  the  sun  ?  page  78. 

15.  What  proofs  can  you  give  of  the  annual  motion  of  the 
earth  ?  page  79. 

16.  What  is  the  distance  of  the  earth  from  the  sun,  and  how 
is  it  calculated  ?  page  80,  and  the  note. 

17.  At  what  rate  per  hour  does  the  earth  travel  around  the 
sun?  page  81. 

18.  At  what  rate  per  hour  are  the  inhabitants  of  the  equator 
carried  from  west  to  east  by  the  revolution  of  the  earth  on  its 
axis,  and  at  what  rate  per  hour  are  the  inhabitants  of  London 
carried  the  same  way  ? 

19.  How  do  you  explain  the  motion  of  the  earth  around  the 
§un  ?  page  81. 

20.  How  do  you  illustrate  the  phenomena  of  the  different  sea- 
sons of  the  year  ?  page  82. 


Chap,  II. 


OF  THE  STUDENT. 


331 


XVI.     OF  THE  MOON,  f). 

I.  How  many  kinds  of  lunar  months  are  there  ?  page  146. 
3.  What  is  a  periodical  month  ?  page  146. 

3.  What  is  a  synodical  month  ? 

4.  When  is  the  eccentricity  of  the  moon's  elliptical  orbit  the 

greatest  ? 

5.  When  is  the  eccentricity  of  the  moon's  elliptical  orbit  the 
least  ? 

().  Whether  does  the  motion  of  the  moon's  nodes  follow,  or 
recede  from  the  order  of  the  signs  ?  page  147. 

7.  In  how  many  years  do  the  moon's  nodes  form  a  complete 
revolution  around  the  ecliptic  ? 

8.  In  what  time  does  the  moon  turn  on  her  axis? 

9.  What  is  the  libration  of  the  moon  ? 

10.  Is  the  path  of  the  moon  convex,  or  concave  towards  the 
sun  ?  page  148. 

II.  Please  to  explain  the  different  phases  of  the  moon  ?  pages 
148  and  149. 

12.  What  point  on  the  earth  has  a  fortnight's  moonlight  and  a 
fortnight's  darkness,  alternately  ?  page  149. 

13.  What  is  the  moon's  mean  horizontal  parallax,  and  at  what 
distance  is  she  from  the  earth  ?  page  150. 

14.  What  is  the  magnitude  of  the  moon  when  compared  with 
that  of  the  earth  ? 

15.  How  many  miles  is  the  moon  in  diameter  ? 

16.  In  how  many  days  does  the  moon  perform  her  revolution 
around  the  earth,  and  at  what  rate  does  she  travel  per  hour  ?  page 
152. 

17.  In  what  manner  have  astronomers  described  the  different 
spots  on  the  moon's  surface  ? 

18.  Have  not  astronomers  discovered  volcanoes,  mountains, 
&c.  in  the  moon  ? 


XVII.  OF  MARS,    ^  . 

1.  What  is  the  general  appearance  of  Mars  ?  page  153. 

2.  In  what  time  does  Mars  revolve  on  his  axis  ? 

3.  In  what  time  does  Mars  perform  his  revolution  around  the 
suii,  and  at  what  rate  does  he  travel  per  hour?  pages  153  and 
154. 


332 


QUESTIONS  FOR  THE  EXAMINATION    ^  Pa7tTV. 


4.  How  far  is  Mars  distant  from  the  sun  ?  page  154. 

5.  How  many  miles  is  Mars  in  diameter? 

6.  What  is  the  comparative  magnitude  of  Mars  and  the 
earth  ? 


XVni.  OF   CERES  5,   PALLAS   ^,  JUNO   0,  AND   VESTA  g, 

1.  When  and  by  whom  w^as  the  planet,  or  Asteroid,  Ceres 
discovered?  page  155. 

2.  How  many  miles  is  Ceres  in  diameter? 

3.  What  is  the  distance  of  Ceres  from  the  sun,  and  what  is 
the  length  of  her  year  ? 

4.  When  and  by  whom  was  Pallas  discovered/'  page  155. 

5.  What  is  the  diameter  of  Pallas  in  English  miles  ? 

6.  What  is  the  distance  of  Pallas  from  the  sun,  and  the  length 
of  her  year  ? 

7.  Who  discovered  the  planet  Juno  ?  page  155. 

8.  How  far  is  Juno  distant  from  the  sun,  and  what  is  the  length 
of  her  year  ? 

9.  By  whom  was  Vesta  discovered  ? 

10.  What  is  the  length  of  Vesta's  year,  and  how  far  is  she  from 
the  sun  ? 


XIX.   OF  JUPITER,   24:,  &C. 

1.  In  what  situation  is  Jupiter  a  morning  star,  and  in  what 
situation  is  he  an  evening  star  ?  page  156. 

2.  In  what  time  does  Jupiter  revolve  on  his  axis  ? 

3.  What  are  Jupiter's  belts  ? 

4.  In  what  time  does  Jupiter  perform  his  revolution  around  the 
sun,  and  at  what  rate  per  hour  does  he  travel  ?  page  156. 

5.  What  is  the  distance  of  Jupiter  from  the  sun.^ 

6.  What  is  the  diameter  of  Jupiter  in  English  miles  ? 

7.  What  is  the  comparative  magnitudes  of  Jupiter  and  the 
earth  ? 

8.  What  is  the  comparison  between  the  light  and  heat  w^hich 
Jupiter  receives  from  the  sun,  and  the  light  and  heat  which  the 
earth  receives  ?  page  157. 

9.  How  many  satellites  is  Jupiter  attended  by?  page  157. 

10.  By  whom  were  the  satellites  of  Jupiter  discovered  ? 


Chap.  II. 


OF  THE  STUDENT. 


333 


II.  In  what  time  do  the  respective  statellites  perform  their  rev- 
olutions around  Jupiter? 

r2.  In  what  manner  are  the  longitudes  of  places  determined 
by  the  statellites  of  Jupiter?  page  157. 

13.  Please  to  explain  the  configuration  of  the  satellites  of  Ju- 
piter as  given  in  the  Xllth  page  of  the  Nautical  Almanac. 

14.  How  was  the  progressive  motion  of  light  discovered? 
page  159. 


XX.   OF  SATURN,  ^,  &LC. 


1.  What  is  the  appearance  of  Saturn  when  viewed  through  a 
telescope  ?  page  160. 

2.  In  what  time  does  Saturn  perform  his  revolution  around 
the  sun,  and  at  what  rate  does  he  travel  per  hour  ? 

3.  What  is  the  distance  of  Saturn  from  the  sun? 

4.  How  many  English  miles  is  Saturn  in  diameter,  and  what  is 
his  magnitude  compared  with  that  of  the  earth?  page  161. 

5.  What  is  the  comparison  between  the  light  and  heat  which 
Saturn  receives  from  the  sun,  and  the  light  and  heat  which  the 
earth  receives  ? 

6.  In  what  time  does  Saturn  revolve  on  his  axis  ? 

7.  How  many  moons  is  Saturn  attended  by,  and  by  whom 
were  they  discovered  ? 

8.  Pray  is  not  the  seventh  satellite  the  nearest  to  Saturn,  and, 
if  so,  why  was  it  not  called  the  first  satellite  ?  page  161. 

9.  What  is  the  ring  of  Saturn,  and  how  may  it  be  represented 
by  the  globe  ?  page  160. 

10.  By  whom  was  the  ring  of  Saturn  discovered? 

11.  In  what  time  does  the  ring  of  Saturn  revolve  around  his 
axis  ? 


XXI.  OF  THE  GEORGIAN  PLANET,  &C. 


1.  When  and  by  whom  was  the  Georgian  planet  discovered? 
page  163. 

5.  What  is  the  appearance  of  the  Georgian  when  viewed 
through  a  telescope  ?  page  163. 


rialrJI. 


I 

I 


/ 


